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%%EndProcSet
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 80 /summationtext put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
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cleartomark
%%EndFont
%%BeginFont: CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: LASY10
%!PS-AdobeFont-1.1: LASY10 1.001
%%CreationDate: 1992 Oct 23 20:19:17
%%RevisionDate: 2001 Jun 05 20:19:17
% Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.001) readonly def
/Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def
/FullName (LASY10) readonly def
/FamilyName (LaTeX) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /LASY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 50 /a50 put
readonly def
/FontBBox{-19 -192 944 683}readonly def
/UniqueID 5011949 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMBX12
%!PS-AdobeFont-1.1: CMBX12 1.0
%%CreationDate: 1991 Aug 20 16:34:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueID 5000769 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY6
%!PS-AdobeFont-1.1: CMSY6 1.0
%%CreationDate: 1991 Aug 15 07:21:34
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
/UniqueID 5000816 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
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end readonly def
/FontName /CMSY10 def
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/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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readonly def
/FontBBox{-29 -960 1116 775}readonly def
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currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMTI10
%!PS-AdobeFont-1.1: CMTI10 1.00B
%%CreationDate: 1992 Feb 19 19:56:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-163 -250 1146 969}readonly def
/UniqueID 5000828 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
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cleartomark
%%EndFont
%%BeginFont: CMMI9
%!PS-AdobeFont-1.1: CMMI9 1.100
%%CreationDate: 1996 Jul 23 07:53:55
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
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end readonly def
/FontName /CMMI9 def
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/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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0 1 255 {1 index exch /.notdef put} for
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readonly def
/FontBBox{-29 -250 1075 750}readonly def
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currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR9
%!PS-AdobeFont-1.1: CMR9 1.0
%%CreationDate: 1991 Aug 20 16:39:59
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-39 -250 1036 750}readonly def
/UniqueID 5000792 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMBX9
%!PS-AdobeFont-1.1: CMBX9 1.0
%%CreationDate: 1991 Aug 20 16:36:25
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX9 def
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/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-58 -250 1195 750}readonly def
/UniqueID 5000767 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.1: CMCSC10 1.0
%%CreationDate: 1991 Aug 18 17:46:49
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMCSC10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{14 -250 1077 750}readonly def
/UniqueID 5000772 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR17
%!PS-AdobeFont-1.1: CMR17 1.0
%%CreationDate: 1991 Aug 20 16:38:24
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR17) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR17 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-33 -250 945 749}readonly def
/UniqueID 5000795 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
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cleartomark
%%EndResource
/F4_0 /CLDCVH+CMR10 1 1
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pdfMakeFont
%%BeginResource: font LBINKS+CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /LBINKS+CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 98 /b put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F7_0 /LBINKS+CMMI10 1 1
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pdfMakeFont
%%BeginResource: font YKUBAT+CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
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end readonly def
/FontName /YKUBAT+CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
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271.673 536.855 m
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292.782 555.018 m
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289.782 554.19 290.453 553.518 291.282 553.518 c
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296.218 582.509 m
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293.218 581.681 293.89 581.009 294.718 581.009 c
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296.218 582.509 m
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293.218 581.681 293.89 581.009 294.718 581.009 c
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273.636 589.382 m
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272.965 587.882 273.636 588.554 273.636 589.382 c
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273.636 589.382 m
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h
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244.155 618.837 m
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Q
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0.4 w
245.627 573.182 m
272.136 589.382 l
294.718 582.509 l
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270.173 536.855 l
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266.763 579.073 m
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266.763 579.073 m
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h
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Q
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284.927 563.855 m
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281.927 563.026 282.599 562.355 283.427 562.355 c
284.256 562.355 284.927 563.026 284.927 563.855 c
h
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284.927 563.855 m
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282.599 565.355 281.927 564.683 281.927 563.855 c
281.927 563.026 282.599 562.355 283.427 562.355 c
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180 615.884 m
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180 615.884 m
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h
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0.4 w
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180.584 580.304 m
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207.363 497.252 m
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f*
205.874 606.353 m
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h
S
Q
q
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392.022 561.638 m
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391.35 560.138 392.022 560.81 392.022 561.638 c
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392.022 561.638 m
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h
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h
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q
330.761 602.475 m
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330.761 602.475 l
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f*
330.761 602.475 m
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330.761 602.475 l
h
S
Q
Q
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0.4 w
355.1 589.873 m
310.378 581.216 l
S
q
310.378 581.216 m
315.604 580.53 l
314.97 583.802 l
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h
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310.378 581.216 m
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310.378 581.216 l
h
S
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q
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351.173 536.364 m
292.37 563.719 l
S
q
292.37 563.719 m
296.2 560.099 l
297.606 563.121 l
292.37 563.719 l
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292.37 563.719 m
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297.606 563.121 l
292.37 563.719 l
h
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q
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262.656 543.209 263.327 543.881 263.327 544.709 c
h
f*
263.327 544.709 m
263.327 545.538 262.656 546.209 261.827 546.209 c
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h
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Q
q
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260.327 543.881 260.999 543.209 261.827 543.209 c
262.656 543.209 263.327 543.881 263.327 544.709 c
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f*
263.327 544.709 m
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260.327 543.881 260.999 543.209 261.827 543.209 c
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h
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Q
q
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271.181 564.345 m
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268.181 563.517 268.853 562.845 269.681 562.845 c
270.51 562.845 271.181 563.517 271.181 564.345 c
h
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271.181 564.345 m
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268.181 563.517 268.853 562.845 269.681 562.845 c
270.51 562.845 271.181 563.517 271.181 564.345 c
h
S
Q
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257.927 564.346 m
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254.927 563.518 255.599 562.846 256.427 562.846 c
257.256 562.846 257.927 563.518 257.927 564.346 c
h
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257.927 564.346 m
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254.927 563.518 255.599 562.846 256.427 562.846 c
257.256 562.846 257.927 563.518 257.927 564.346 c
h
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283.427 563.855 l
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265.264 579.073 l
S
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261.309 558.608 261.981 557.937 262.809 557.937 c
263.638 557.937 264.309 558.608 264.309 559.437 c
h
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264.309 559.437 m
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261.981 560.937 261.309 560.265 261.309 559.437 c
261.309 558.608 261.981 557.937 262.809 557.937 c
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h
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q
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272.63 554.284 l
S
q
272.63 554.284 m
274.928 549.541 l
277.314 551.868 l
272.63 554.284 l
h
f*
272.63 554.284 m
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277.314 551.868 l
272.63 554.284 l
h
S
Q
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q
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364.636 545.667 365.307 544.996 366.136 544.996 c
366.964 544.996 367.636 545.667 367.636 546.496 c
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367.636 546.496 m
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364.636 545.667 365.307 544.996 366.136 544.996 c
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h
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384.15 509.331 384.822 508.659 385.65 508.659 c
386.478 508.659 387.15 509.331 387.15 510.159 c
h
f*
387.15 510.159 m
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384.15 509.331 384.822 508.659 385.65 508.659 c
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h
S
Q
q
0.4 w
Q
q
0.4 w
Q
q
0.4 w
Q
q
[1 0 0 1 350.398 611.024] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(con) 14.9445 Tj
28 TJm
(v) 5.26046 Tj
20.064 0 Td
/F7_0 9.963 Tf
(A) 7.47225 Tj
Q
q
[1 0 0 1 358.953 586.785] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(con) 14.9445 Tj
28 TJm
(v) 5.26046 Tj
20.064 0 Td
/F7_0 9.963 Tf
(B) 7.55195 Tj
Q
q
[1 0 0 1 356.101 532.608] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(con) 14.9445 Tj
28 TJm
(v) 5.26046 Tj
20.064 0 Td
/F7_0 9.963 Tf
(C) 7.12355 Tj
Q
q
[1 0 0 1 329.725 489.123] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(con) 14.9445 Tj
28 TJm
(v) 5.26046 Tj
20.064 0 Td
/F7_0 9.963 Tf
(D) 8.24936 Tj
Q
q
[1 0 0 1 251.766 606.721] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F7_0 9.963 Tf
(b) 4.27413 Tj
4.276 -1.494 Td
/F10_0 6.974 Tf
(1) 3.96821 Tj
Q
q
[1 0 0 1 309.946 601.594] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F7_0 9.963 Tf
(b) 4.27413 Tj
4.276 -1.494 Td
/F10_0 6.974 Tf
(2) 3.96821 Tj
Q
q
[1 0 0 1 319.754 556.121] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F7_0 9.963 Tf
(b) 4.27413 Tj
4.276 -1.494 Td
/F10_0 6.974 Tf
(3) 3.96821 Tj
Q
q
[1 0 0 1 303.481 524.245] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
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0 0 Td
/F7_0 9.963 Tf
(b) 4.27413 Tj
4.276 -1.494 Td
/F10_0 6.974 Tf
(4) 3.96821 Tj
Q
q
[1 0 0 1 259.568 505.966] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F7_0 9.963 Tf
(b) 4.27413 Tj
4.276 -1.494 Td
/F10_0 6.974 Tf
(5) 3.96821 Tj
Q
q
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[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F7_0 9.963 Tf
(b) 4.27413 Tj
4.276 -1.494 Td
/F10_0 6.974 Tf
(6) 3.96821 Tj
Q
q
[1 0 0 1 219.667 581.978] cm
[1 0 0 1 0 2.85] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
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(b) 4.27413 Tj
4.276 -1.494 Td
/F13_0 6.974 Tf
(\014) 4.51915 Tj
12.417 0 Td
/F4_0 9.963 Tf
(=) 7.75121 Tj
22.933 0 Td
/F7_0 9.963 Tf
(b) 4.27413 Tj
27.209 -1.494 Td
/F10_0 6.974 Tf
(7) 3.96821 Tj
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@endspecial 1184 2992 a(Figure)g(1:)37 b(The)27 b(\\la)n(y)n(ers")e
Fm(A)p Fn(,)j Fm(B)t Fn(,)g Fm(C)6 b Fn(,)28 b Fm(D)r
Fn(.)455 3187 y(Here)f(is)g(our)g(k)n(ey)g(lemma:)330
3369 y Fk(Lemma)32 b(1)41 b Fl(If)30 b Fm(P)42 b Fl(has)30
b(no)g Fn(6)p Fl(-hole)g(and)g Fj(j)p Fm(A)p Fj(j)24
b(\025)e Fn(7)30 b Fl(then)f Fm(D)c Fn(=)e Fj(;)p Fl(.)455
3552 y Fn(Before)32 b(pro)n(ving)h(Lemma)g(1,)i(w)n(e)f(sho)n(w)f(that)
h(it)g(easily)f(implies)h(Theorem)f(2)h(with)g Fm(c)f
Fn(=)330 3652 y(ES\(216\))623 3621 y Fg(1)659 3652 y
Fn(.)63 b(Let)37 b Fj(j)p Fm(P)12 b Fj(j)37 b(\025)h
Fn(ES)o(\(216\),)g(and)e(let)h Fm(A)g Fn(b)r(e)g(the)f(v)n(ertex)g(set)
g(of)h(an)n(y)e(minimal)i(216-)330 3751 y(gon.)72 b(Lemma)39
b(1)g(giv)n(es)f Fm(D)45 b Fn(=)e Fj(;)p Fn(.)72 b(It)40
b(follo)n(ws)e(that)i Fj(j)p Fm(C)6 b Fj(j)43 b(\024)g
Fn(5,)f(since)d(otherwise)g(an)n(y)f(six)330 3851 y(v)n(ertices)28
b(of)i Fm(C)36 b Fn(w)n(ould)29 b(form)g(a)g(6-hole.)42
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pdfMakeFont16
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/l { lineto } def
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% path painting operators
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{ currentfile pdfImBuf1 readhexstring pop }
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{ currentfile pdfImBuf3 readhexstring pop }
{ currentfile pdfImBuf4 readhexstring pop }
true 4 colorimage
} def
/pdfImM1 {
/pdfImBuf1 4 index 7 add 8 idiv string def
{ currentfile pdfImBuf1 readhexstring pop } imagemask
} def
% Level 2 image operators
/pdfImBuf 100 string def
/pdfIm {
image
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
/pdfImSep {
findcmykcustomcolor exch
dup /Width get /pdfImBuf1 exch string def
begin Width Height BitsPerComponent ImageMatrix DataSource end
/pdfImData exch def
{ pdfImData pdfImBuf1 readstring pop
0 1 2 index length 1 sub {
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6 5 roll customcolorimage
{ currentfile pdfImBuf readline
not { pop exit } if
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/pdfImM {
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cleartomark
%%EndResource
/F7_0 /VROIUY+CMR7 1 1
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pdfMakeFont
%%BeginResource: font IAYPQC+CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /IAYPQC+CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 107 /k put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F10_0 /IAYPQC+CMMI7 1 1
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pdfMakeFont
%%BeginResource: font KESORX+CMMI9
%!PS-AdobeFont-1.1: CMMI9 1.100
%%CreationDate: 1996 Jul 23 07:53:55
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /KESORX+CMMI9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 58 /period put
dup 59 /comma put
dup 83 /S put
dup 112 /p put
readonly def
/FontBBox{-29 -250 1075 750}readonly def
/UniqueID 5087384 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F13_0 /KESORX+CMMI9 1 1
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font JQUDTW+CMR9
%!PS-AdobeFont-1.1: CMR9 1.0
%%CreationDate: 1991 Aug 20 16:39:59
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /JQUDTW+CMR9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright put
readonly def
/FontBBox{-39 -250 1036 750}readonly def
/UniqueID 5000792 def
currentdict end
currentfile eexec
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pdfMakeFont
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pdfMakeFont
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%%CreationDate: 1996 Jul 23 07:53:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
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cleartomark
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%
%
%
%
%
%
%
%
%
%
%
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%
%
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%
%
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%
%
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%
%
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%
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pdfStartPage
[] 0 d
0 i
0 j
0 J
10 M
1 w
0 g
0 G
202.735 396.439 115.181 129.492 re
W
q
q
0.4 w
205.363 435.932 m
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h
f*
205.363 435.932 m
205.363 436.76 204.691 437.432 203.863 437.432 c
203.035 437.432 202.363 436.76 202.363 435.932 c
202.363 435.103 203.035 434.432 203.863 434.432 c
204.691 434.432 205.363 435.103 205.363 435.932 c
h
S
Q
q
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@endspecial 1449 1656 a Fn(Figure)27 b(2:)36 b(A)28
b Fm(k)s Fn(-sector.)330 1921 y Fk(Observ)-5 b(ation)31
b(2)42 b Fl(If)33 b(a)g(c)l(onvex)f(p)l(entagon)h Fm(p)1783
1933 y Fg(1)1820 1921 y Fm(p)1862 1933 y Fg(2)1899 1921
y Fm(p)1941 1933 y Fg(3)1978 1921 y Fm(p)2020 1933 y
Fg(4)2057 1921 y Fm(p)2099 1933 y Fg(5)2169 1921 y Fl(with)g(vertic)l
(es)g(in)g Fm(P)44 b Fl(is)33 b(empty)g(and)330 2021
y Fm(q)26 b Fj(2)e Fm(P)30 b Fj(\\)19 b Fm(S)5 b Fn(\()p
Fm(p)759 2033 y Fg(1)796 2021 y Fm(;)14 b(p)875 2033
y Fg(2)912 2021 y Fm(;)g(p)991 2033 y Fg(4)1027 2021
y Fm(;)g(p)1106 2033 y Fg(5)1143 2021 y Fn(\))p Fl(,)31
b(then)e Fm(P)42 b Fl(c)l(ontains)30 b(a)g Fn(6)p Fl(-hole.)330
2204 y(Pr)l(o)l(of.)115 b Fn(If)38 b(the)g(triangle)e
Fm(q)s(p)1304 2216 y Fg(1)1341 2204 y Fm(p)1383 2216
y Fg(5)1458 2204 y Fn(is)h(empt)n(y)h(then)g Fm(q)s(p)2096
2216 y Fg(1)2133 2204 y Fm(p)2175 2216 y Fg(2)2212 2204
y Fm(p)2254 2216 y Fg(3)2291 2204 y Fm(p)2333 2216 y
Fg(4)2370 2204 y Fm(p)2412 2216 y Fg(5)2486 2204 y Fn(is)g(a)f(6-hole.)
65 b(Otherwise)330 2303 y Fm(r)r(p)411 2315 y Fg(1)449
2303 y Fm(p)491 2315 y Fg(2)528 2303 y Fm(p)570 2315
y Fg(3)607 2303 y Fm(p)649 2315 y Fg(4)686 2303 y Fm(p)728
2315 y Fg(5)793 2303 y Fn(is)27 b(a)g(6-hole)g(for)g(some)g
Fm(r)f Fj(2)d Fm(P)39 b Fn(inside)28 b(the)g(triangle)f
Fm(q)s(p)2524 2315 y Fg(1)2561 2303 y Fm(p)2603 2315
y Fg(5)2640 2303 y Fn(.)37 b Ff(2)330 2536 y Fh(2.3)112
b(Pro)s(of)37 b(of)h(Lemma)h(1)330 2689 y Fn(Set)23 b
Fm(\013)h Fn(:=)f Fj(j)p Fm(A)p Fj(j)p Fm(;)14 b(\014)27
b Fn(:=)c Fj(j)p Fm(B)t Fj(j)p Fn(.)36 b(W)-7 b(e)23
b(will)g(sho)n(w)g(that)g(if)h Fm(\013)f Fj(\025)g Fn(7)f(and)h
Fm(D)i Fj(6)p Fn(=)e Fj(;)g Fn(then)g(either)g Fm(P)35
b Fn(con)n(tains)330 2789 y(a)27 b(6-hole)g(or)f(con)n(v)q
Fm(A)h Fn(is)h(not)g(minimal.)455 2888 y(Supp)r(ose)i
Fm(D)h Fj(6)p Fn(=)d Fj(;)j Fn(and)f(\014x)h(an)g(arbitrary)e(p)r(oin)n
(t)i Fm(d)e Fj(2)g Fm(D)r Fn(.)47 b(Denote)31 b(the)g(v)n(ertices)f(of)
h Fm(B)k Fn(in)330 2988 y(the)c(clo)r(c)n(kwise)f(order)f(b)n(y)h
Fm(b)1216 3000 y Fg(1)1253 2988 y Fm(;)14 b(b)1326 3000
y Fg(2)1363 2988 y Fm(;)g(:)g(:)g(:)f(;)h(b)1583 3000
y Fe(\014)1658 2988 y Fn(\(see)31 b(Figure)f(1\).)46
b(F)-7 b(or)30 b Fm(i)d Fn(=)h(1)p Fm(;)14 b(:)g(:)g(:)f(;)h(\014)t
Fn(,)32 b(let)f Fm(T)3041 3000 y Fe(i)3099 2988 y Fn(b)r(e)g(the)330
3087 y(triangle)i Fm(db)720 3099 y Fe(i)747 3087 y Fm(b)783
3099 y Fe(i)p Fg(+1)928 3087 y Fn(\(see)h(Figure)f(3;)j(w)n(e)e(alw)n
(a)n(ys)d(iden)n(tify)k(the)f(indices)f(in)h(a)f(natural)g(w)n(a)n(y)g
(so)330 3187 y(that)28 b Fm(b)546 3199 y Fe(i)596 3187
y Fn(=)23 b Fm(b)720 3199 y Fe(\014)s Fg(+)p Fe(i)866
3187 y Fn(for)k(an)n(y)g(in)n(teger)g Fm(i)p Fn(\).)651
4652 y @beginspecial 137 @llx 486 @lly 420 @urx 647 @ury
2830 @rwi @setspecial
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cleartomark
%%EndResource
/F4_0 /DQGEYA+CMR10 1 1
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font CMYDXA+CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMYDXA+CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 84 /T put
dup 98 /b put
dup 99 /c put
dup 100 /d put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F7_0 /CMYDXA+CMMI10 1 1
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font VWEROQ+CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /VWEROQ+CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 105 /i put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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5109 y Fj(2)e Fm(C)e Fj(\\)21 b Fm(T)3112 5121 y Fe(i)3170
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Fm(c)2853 5221 y Fe(i)2904 5209 y Fn(as)h(the)h(p)r(oin)n(t)330
5309 y(of)k Fm(C)c Fj(\\)19 b Fm(T)631 5321 y Fe(i)686
5309 y Fn(closest)27 b(to)g(the)h(line)g Fm(b)1387 5321
y Fe(i)1414 5309 y Fm(b)1450 5321 y Fe(i)p Fg(+1)1562
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cleartomark
%%EndResource
/F4_0 /NCXJYD+CMR10 1 1
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font XHBZKK+CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /XHBZKK+CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 82 /R put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F7_0 /XHBZKK+CMMI10 1 1
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/.notdef/.notdef/R/.notdef/T/.notdef/.notdef/.notdef
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font RAJLXP+CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /RAJLXP+CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 105 /i put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F10_0 /RAJLXP+CMMI7 1 1
[ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font ZCVPDZ+CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /ZCVPDZ+CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 43 /plus put
dup 49 /one put
dup 50 /two put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F13_0 /ZCVPDZ+CMR7 1 1
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pdfMakeFont
%%BeginResource: font LEJYUA+CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /LEJYUA+CMSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 48 /prime put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F16_0 /LEJYUA+CMSY7 1 1
[ /minus/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
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/prime/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
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pdfMakeFont
%%EndSetup
%
%
%
%
%
%
%
%
%
%
%
%
%257.096 644.109 m
%333.5 623.091 l
%356.979 578.604 l
%349.741 534.794 l
%323.455 506.223 l
%263.136 488.909 l
%217.931 501.652 l
%193.55 534.414 l
%198.957 613.692 l
%257.096 644.109 l
%
%
%257.931 607.175 m
%287.646 612.785 l
%315.607 600.902 l
%329.931 585.08 l
%305.55 519.937 l
%270.122 516.509 l
%240.407 530.604 l
%235.836 573.652 l
%257.931 607.175 l
%
%conv$B$
%conv$C$
%
%172.447 591.211 m
%197.483 592.088 l
%
%
%173.079 564.053 m
%237.061 562.118 l
%
%
%
%256.487 588.355 m
%292.299 589.486 l
%297.169 554.223 l
%258.227 534.727 l
%249.227 567.455 l
%256.487 588.355 l
%
%conv$D$
%
%173.079 540.684 m
%252.543 555.398 l
%
%
%419.395 646.789 m
%419.395 646.789 l h
%
%$d$
%
%
%$c$
%
%
%
%
%
%
%
%256.487 588.355 m
%323.455 506.223 l
%
%
%256.487 588.355 m
%349.741 534.794 l
%
%
%
%
%
%
%
%
%
%
%$b_i$
%$b_{i+1}$
%
%
%
%256.487 588.355 m
%323.455 506.223 l
%
%
%256.487 588.355 m
%356.979 578.604 l
%
%
%256.487 588.355 m
%349.741 534.794 l
%
%
%
%329.931 585.08 m
%356.979 578.604 l
%349.741 534.794 l
%323.455 506.223 l
%305.55 519.937 l h
%
%$b_{i+2}$
%$c'$
%
%467.395 574.158 m
%488.972 541.967 l
%512.868 540.053 l
%521.756 562.762 l
%501.5 591.842 l h
%
%
%509.711 605.105 m
%519.816 648.684 l
%
%
%453.268 574.925 m
%413.079 587.421 l
%
%
%519.23 547.604 m
%546.974 578.579 l
%
%
%486.445 526.809 m
%429.5 521.737 l
%
%$d$
%$c$
%$b_i$
%$a$
%$b_{i+1}$
%$c'$
%
%488.972 541.967 m
%521.757 562.761 l
%
%$R_i$
%${\rm conv}B$
%${\rm conv} C$
%
%446.553 519.211 m
%447.412 538.265 l
%
%
%419.395 554.579 m
%432.442 581.4 l
%
%
%
%
%488.972 541.967 m
%540.103 494.768 l
%521.757 562.761 l
%
%
%453.268 574.925 m
%488.972 541.967 l
%
%
%509.711 605.105 m
%521.756 562.762 l
%
%
%453.268 574.925 m
%467.395 574.158 l
%
%
%501.5 591.842 m
%509.711 605.105 l
%
%$c_{i-1}$
%$c_{i+1}$
%
%$T_i$
%$T_{i+1}$
%$T_i$
%
%
%
pdfStartPage
[] 0 d
0 i
0 j
0 J
10 M
1 w
0 g
0 G
137.908 487.112 411.592 174.835 re
W
q
q
0.4 w
258.596 644.11 m
258.596 644.938 257.924 645.61 257.096 645.61 c
256.267 645.61 255.596 644.938 255.596 644.11 c
255.596 643.281 256.267 642.61 257.096 642.61 c
257.924 642.61 258.596 643.281 258.596 644.11 c
h
f*
258.596 644.11 m
258.596 644.938 257.924 645.61 257.096 645.61 c
256.267 645.61 255.596 644.938 255.596 644.11 c
255.596 643.281 256.267 642.61 257.096 642.61 c
257.924 642.61 258.596 643.281 258.596 644.11 c
h
S
Q
q
0.4 w
200.457 613.692 m
200.457 614.521 199.785 615.192 198.957 615.192 c
198.128 615.192 197.457 614.521 197.457 613.692 c
197.457 612.864 198.128 612.192 198.957 612.192 c
199.785 612.192 200.457 612.864 200.457 613.692 c
h
f*
200.457 613.692 m
200.457 614.521 199.785 615.192 198.957 615.192 c
198.128 615.192 197.457 614.521 197.457 613.692 c
197.457 612.864 198.128 612.192 198.957 612.192 c
199.785 612.192 200.457 612.864 200.457 613.692 c
h
S
Q
q
0.4 w
219.431 501.652 m
219.431 502.48 218.76 503.152 217.931 503.152 c
217.103 503.152 216.431 502.48 216.431 501.652 c
216.431 500.823 217.103 500.152 217.931 500.152 c
218.76 500.152 219.431 500.823 219.431 501.652 c
h
f*
219.431 501.652 m
219.431 502.48 218.76 503.152 217.931 503.152 c
217.103 503.152 216.431 502.48 216.431 501.652 c
216.431 500.823 217.103 500.152 217.931 500.152 c
218.76 500.152 219.431 500.823 219.431 501.652 c
h
S
Q
q
0.4 w
335 623.091 m
335 623.919 334.328 624.591 333.5 624.591 c
332.672 624.591 332 623.919 332 623.091 c
332 622.263 332.672 621.591 333.5 621.591 c
334.328 621.591 335 622.263 335 623.091 c
h
f*
335 623.091 m
335 623.919 334.328 624.591 333.5 624.591 c
332.672 624.591 332 623.919 332 623.091 c
332 622.263 332.672 621.591 333.5 621.591 c
334.328 621.591 335 622.263 335 623.091 c
h
S
Q
q
0.4 w
259.431 607.175 m
259.431 608.004 258.76 608.675 257.931 608.675 c
257.103 608.675 256.431 608.004 256.431 607.175 c
256.431 606.347 257.103 605.675 257.931 605.675 c
258.76 605.675 259.431 606.347 259.431 607.175 c
h
f*
259.431 607.175 m
259.431 608.004 258.76 608.675 257.931 608.675 c
257.103 608.675 256.431 608.004 256.431 607.175 c
256.431 606.347 257.103 605.675 257.931 605.675 c
258.76 605.675 259.431 606.347 259.431 607.175 c
h
S
Q
q
0.4 w
237.336 573.652 m
237.336 574.48 236.664 575.152 235.836 575.152 c
235.007 575.152 234.336 574.48 234.336 573.652 c
234.336 572.823 235.007 572.152 235.836 572.152 c
236.664 572.152 237.336 572.823 237.336 573.652 c
h
f*
237.336 573.652 m
237.336 574.48 236.664 575.152 235.836 575.152 c
235.007 575.152 234.336 574.48 234.336 573.652 c
234.336 572.823 235.007 572.152 235.836 572.152 c
236.664 572.152 237.336 572.823 237.336 573.652 c
h
S
Q
q
0.4 w
289.146 612.785 m
289.146 613.614 288.475 614.285 287.646 614.285 c
286.818 614.285 286.146 613.614 286.146 612.785 c
286.146 611.957 286.818 611.285 287.646 611.285 c
288.475 611.285 289.146 611.957 289.146 612.785 c
h
f*
289.146 612.785 m
289.146 613.614 288.475 614.285 287.646 614.285 c
286.818 614.285 286.146 613.614 286.146 612.785 c
286.146 611.957 286.818 611.285 287.646 611.285 c
288.475 611.285 289.146 611.957 289.146 612.785 c
h
S
Q
q
0.4 w
257.096 644.109 m
333.5 623.091 l
356.979 578.604 l
349.741 534.794 l
323.455 506.223 l
263.136 488.909 l
217.931 501.652 l
193.55 534.414 l
198.957 613.692 l
257.096 644.109 l
S
Q
q
0.4 w
257.931 607.175 m
287.646 612.785 l
315.607 600.902 l
329.931 585.08 l
305.55 519.937 l
270.122 516.509 l
240.407 530.604 l
235.836 573.652 l
257.931 607.175 l
S
Q
q
[1 0 0 1 138.109 587.404] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(con) 14.9445 Tj
28 TJm
(v) 5.26046 Tj
19.925 0 Td
/F7_0 9.963 Tf
(B) 7.55195 Tj
Q
q
[1 0 0 1 138.153 562.119] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(con) 14.9445 Tj
28 TJm
(v) 5.26046 Tj
19.925 0 Td
/F7_0 9.963 Tf
(C) 7.12355 Tj
Q
q
0.4 w
172.447 591.211 m
197.483 592.088 l
S
q
197.483 592.088 m
192.428 593.579 l
192.544 590.247 l
197.483 592.088 l
h
f*
197.483 592.088 m
192.428 593.579 l
192.544 590.247 l
197.483 592.088 l
h
S
Q
Q
q
0.4 w
173.079 564.053 m
237.061 562.118 l
S
q
237.061 562.118 m
232.114 563.935 l
232.013 560.603 l
237.061 562.118 l
h
f*
237.061 562.118 m
232.114 563.935 l
232.013 560.603 l
237.061 562.118 l
h
S
Q
Q
q
0.4 w
250.727 567.455 m
250.727 568.283 250.055 568.955 249.227 568.955 c
248.399 568.955 247.727 568.283 247.727 567.455 c
247.727 566.627 248.399 565.955 249.227 565.955 c
250.055 565.955 250.727 566.627 250.727 567.455 c
h
f*
250.727 567.455 m
250.727 568.283 250.055 568.955 249.227 568.955 c
248.399 568.955 247.727 568.283 247.727 567.455 c
247.727 566.627 248.399 565.955 249.227 565.955 c
250.055 565.955 250.727 566.627 250.727 567.455 c
h
S
Q
q
0.4 w
256.487 588.355 m
292.299 589.486 l
297.169 554.223 l
258.227 534.727 l
249.227 567.455 l
256.487 588.355 l
S
Q
q
[1 0 0 1 137.908 536.141] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(con) 14.9445 Tj
28 TJm
(v) 5.26046 Tj
19.925 0 Td
/F7_0 9.963 Tf
(D) 8.24936 Tj
Q
q
0.4 w
173.079 540.684 m
252.543 555.398 l
S
q
252.543 555.398 m
247.323 556.126 l
247.93 552.849 l
252.543 555.398 l
h
f*
252.543 555.398 m
247.323 556.126 l
247.93 552.849 l
252.543 555.398 l
h
S
Q
Q
q
2 w
421.921 661.947 m
421.921 661.947 l
h
S
Q
q
[1 0 0 1 248.149 584.333] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F7_0 9.963 Tf
(d) 5.18076 Tj
Q
q
0.4 w
241.907 530.604 m
241.907 531.432 241.235 532.104 240.407 532.104 c
239.579 532.104 238.907 531.432 238.907 530.604 c
238.907 529.776 239.579 529.104 240.407 529.104 c
241.235 529.104 241.907 529.776 241.907 530.604 c
h
f*
241.907 530.604 m
241.907 531.432 241.235 532.104 240.407 532.104 c
239.579 532.104 238.907 531.432 238.907 530.604 c
238.907 529.776 239.579 529.104 240.407 529.104 c
241.235 529.104 241.907 529.776 241.907 530.604 c
h
S
Q
q
0.4 w
195.05 534.414 m
195.05 535.242 194.378 535.914 193.55 535.914 c
192.722 535.914 192.05 535.242 192.05 534.414 c
192.05 533.586 192.722 532.914 193.55 532.914 c
194.378 532.914 195.05 533.586 195.05 534.414 c
h
f*
195.05 534.414 m
195.05 535.242 194.378 535.914 193.55 535.914 c
192.722 535.914 192.05 535.242 192.05 534.414 c
192.05 533.586 192.722 532.914 193.55 532.914 c
194.378 532.914 195.05 533.586 195.05 534.414 c
h
S
Q
q
[1 0 0 1 330.488 589.702] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F7_0 9.963 Tf
(c) 4.31398 Tj
Q
q
0.4 w
490.472 541.967 m
490.472 542.796 489.8 543.467 488.972 543.467 c
488.143 543.467 487.472 542.796 487.472 541.967 c
487.472 541.139 488.143 540.467 488.972 540.467 c
489.8 540.467 490.472 541.139 490.472 541.967 c
h
f*
490.472 541.967 m
490.472 542.796 489.8 543.467 488.972 543.467 c
488.143 543.467 487.472 542.796 487.472 541.967 c
487.472 541.139 488.143 540.467 488.972 540.467 c
489.8 540.467 490.472 541.139 490.472 541.967 c
h
S
Q
q
0.4 w
523.256 562.762 m
523.256 563.59 522.585 564.262 521.756 564.262 c
520.928 564.262 520.256 563.59 520.256 562.762 c
520.256 561.934 520.928 561.262 521.756 561.262 c
522.585 561.262 523.256 561.934 523.256 562.762 c
h
f*
523.256 562.762 m
523.256 563.59 522.585 564.262 521.756 564.262 c
520.928 564.262 520.256 563.59 520.256 562.762 c
520.256 561.934 520.928 561.262 521.756 561.262 c
522.585 561.262 523.256 561.934 523.256 562.762 c
h
S
Q
q
0.4 w
514.368 540.053 m
514.368 540.881 513.697 541.553 512.868 541.553 c
512.04 541.553 511.368 540.881 511.368 540.053 c
511.368 539.224 512.04 538.553 512.868 538.553 c
513.697 538.553 514.368 539.224 514.368 540.053 c
h
f*
514.368 540.053 m
514.368 540.881 513.697 541.553 512.868 541.553 c
512.04 541.553 511.368 540.881 511.368 540.053 c
511.368 539.224 512.04 538.553 512.868 538.553 c
513.697 538.553 514.368 539.224 514.368 540.053 c
h
S
Q
q
0.4 w
447.043 638.634 m
447.043 639.462 446.371 640.134 445.543 640.134 c
444.714 640.134 444.043 639.462 444.043 638.634 c
444.043 637.805 444.714 637.134 445.543 637.134 c
446.371 637.134 447.043 637.805 447.043 638.634 c
h
f*
447.043 638.634 m
447.043 639.462 446.371 640.134 445.543 640.134 c
444.714 640.134 444.043 639.462 444.043 638.634 c
444.043 637.805 444.714 637.134 445.543 637.134 c
446.371 637.134 447.043 637.805 447.043 638.634 c
h
S
Q
q
0.4 w
511.21 605.106 m
511.21 605.934 510.539 606.606 509.71 606.606 c
508.882 606.606 508.21 605.934 508.21 605.106 c
508.21 604.277 508.882 603.606 509.71 603.606 c
510.539 603.606 511.21 604.277 511.21 605.106 c
h
f*
511.21 605.106 m
511.21 605.934 510.539 606.606 509.71 606.606 c
508.882 606.606 508.21 605.934 508.21 605.106 c
508.21 604.277 508.882 603.606 509.71 603.606 c
510.539 603.606 511.21 604.277 511.21 605.106 c
h
S
Q
q
0.4 w
454.768 574.925 m
454.768 575.754 454.097 576.425 453.268 576.425 c
452.44 576.425 451.768 575.754 451.768 574.925 c
451.768 574.097 452.44 573.425 453.268 573.425 c
454.097 573.425 454.768 574.097 454.768 574.925 c
h
f*
454.768 574.925 m
454.768 575.754 454.097 576.425 453.268 576.425 c
452.44 576.425 451.768 575.754 451.768 574.925 c
451.768 574.097 452.44 573.425 453.268 573.425 c
454.097 573.425 454.768 574.097 454.768 574.925 c
h
S
Q
q
[1 3] 0 d
0.4 w
445.543 638.634 m
488.972 541.968 l
S
Q
q
[1 3] 0 d
0.4 w
445.543 638.634 m
521.757 562.762 l
S
Q
q
0.4 w
264.636 488.909 m
264.636 489.737 263.964 490.409 263.136 490.409 c
262.308 490.409 261.636 489.737 261.636 488.909 c
261.636 488.081 262.308 487.409 263.136 487.409 c
263.964 487.409 264.636 488.081 264.636 488.909 c
h
f*
264.636 488.909 m
264.636 489.737 263.964 490.409 263.136 490.409 c
262.308 490.409 261.636 489.737 261.636 488.909 c
261.636 488.081 262.308 487.409 263.136 487.409 c
263.964 487.409 264.636 488.081 264.636 488.909 c
h
S
Q
q
0.4 w
324.955 506.223 m
324.955 507.051 324.283 507.723 323.455 507.723 c
322.626 507.723 321.955 507.051 321.955 506.223 c
321.955 505.395 322.626 504.723 323.455 504.723 c
324.283 504.723 324.955 505.395 324.955 506.223 c
h
f*
324.955 506.223 m
324.955 507.051 324.283 507.723 323.455 507.723 c
322.626 507.723 321.955 507.051 321.955 506.223 c
321.955 505.395 322.626 504.723 323.455 504.723 c
324.283 504.723 324.955 505.395 324.955 506.223 c
h
S
Q
q
0.4 w
351.241 534.794 m
351.241 535.623 350.569 536.294 349.741 536.294 c
348.912 536.294 348.241 535.623 348.241 534.794 c
348.241 533.966 348.912 533.294 349.741 533.294 c
350.569 533.294 351.241 533.966 351.241 534.794 c
h
f*
351.241 534.794 m
351.241 535.623 350.569 536.294 349.741 536.294 c
348.912 536.294 348.241 535.623 348.241 534.794 c
348.241 533.966 348.912 533.294 349.741 533.294 c
350.569 533.294 351.241 533.966 351.241 534.794 c
h
S
Q
q
0.4 w
358.479 578.604 m
358.479 579.432 357.807 580.104 356.979 580.104 c
356.15 580.104 355.479 579.432 355.479 578.604 c
355.479 577.776 356.15 577.104 356.979 577.104 c
357.807 577.104 358.479 577.776 358.479 578.604 c
h
f*
358.479 578.604 m
358.479 579.432 357.807 580.104 356.979 580.104 c
356.15 580.104 355.479 579.432 355.479 578.604 c
355.479 577.776 356.15 577.104 356.979 577.104 c
357.807 577.104 358.479 577.776 358.479 578.604 c
h
S
Q
q
0.4 w
331.431 585.08 m
331.431 585.909 330.76 586.58 329.931 586.58 c
329.103 586.58 328.431 585.909 328.431 585.08 c
328.431 584.252 329.103 583.58 329.931 583.58 c
330.76 583.58 331.431 584.252 331.431 585.08 c
h
f*
331.431 585.08 m
331.431 585.909 330.76 586.58 329.931 586.58 c
329.103 586.58 328.431 585.909 328.431 585.08 c
328.431 584.252 329.103 583.58 329.931 583.58 c
330.76 583.58 331.431 584.252 331.431 585.08 c
h
S
Q
q
0.4 w
257.987 588.355 m
257.987 589.184 257.315 589.855 256.487 589.855 c
255.659 589.855 254.987 589.184 254.987 588.355 c
254.987 587.527 255.659 586.855 256.487 586.855 c
257.315 586.855 257.987 587.527 257.987 588.355 c
h
f*
257.987 588.355 m
257.987 589.184 257.315 589.855 256.487 589.855 c
255.659 589.855 254.987 589.184 254.987 588.355 c
254.987 587.527 255.659 586.855 256.487 586.855 c
257.315 586.855 257.987 587.527 257.987 588.355 c
h
S
Q
q
0.4 w
259.727 534.727 m
259.727 535.555 259.055 536.227 258.227 536.227 c
257.399 536.227 256.727 535.555 256.727 534.727 c
256.727 533.899 257.399 533.227 258.227 533.227 c
259.055 533.227 259.727 533.899 259.727 534.727 c
h
f*
259.727 534.727 m
259.727 535.555 259.055 536.227 258.227 536.227 c
257.399 536.227 256.727 535.555 256.727 534.727 c
256.727 533.899 257.399 533.227 258.227 533.227 c
259.055 533.227 259.727 533.899 259.727 534.727 c
h
S
Q
q
0.4 w
259.727 534.727 m
259.727 535.555 259.055 536.227 258.227 536.227 c
257.399 536.227 256.727 535.555 256.727 534.727 c
256.727 533.899 257.399 533.227 258.227 533.227 c
259.055 533.227 259.727 533.899 259.727 534.727 c
h
f*
259.727 534.727 m
259.727 535.555 259.055 536.227 258.227 536.227 c
257.399 536.227 256.727 535.555 256.727 534.727 c
256.727 533.899 257.399 533.227 258.227 533.227 c
259.055 533.227 259.727 533.899 259.727 534.727 c
h
S
Q
q
0.4 w
293.799 589.486 m
293.799 590.314 293.127 590.986 292.299 590.986 c
291.47 590.986 290.799 590.314 290.799 589.486 c
290.799 588.658 291.47 587.986 292.299 587.986 c
293.127 587.986 293.799 588.658 293.799 589.486 c
h
f*
293.799 589.486 m
293.799 590.314 293.127 590.986 292.299 590.986 c
291.47 590.986 290.799 590.314 290.799 589.486 c
290.799 588.658 291.47 587.986 292.299 587.986 c
293.127 587.986 293.799 588.658 293.799 589.486 c
h
S
Q
q
[1 0 0 1 364.884 573.531] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F7_0 9.963 Tf
(b) 4.27413 Tj
4.276 -1.494 Td
/F10_0 6.974 Tf
(i) 2.8175 Tj
Q
q
[1 0 0 1 358.115 526.353] cm
[1 0 0 1 0 2.325] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F7_0 9.963 Tf
(b) 4.27413 Tj
4.276 -1.495 Td
/F10_0 6.974 Tf
(i) 2.8175 Tj
7.094 -1.495 Td
/F13_0 6.974 Tf
(+1) 10.0844 Tj
Q
q
0.4 w
298.669 554.223 m
298.669 555.052 297.998 555.723 297.169 555.723 c
296.341 555.723 295.669 555.052 295.669 554.223 c
295.669 553.395 296.341 552.723 297.169 552.723 c
297.998 552.723 298.669 553.395 298.669 554.223 c
h
f*
298.669 554.223 m
298.669 555.052 297.998 555.723 297.169 555.723 c
296.341 555.723 295.669 555.052 295.669 554.223 c
295.669 553.395 296.341 552.723 297.169 552.723 c
297.998 552.723 298.669 553.395 298.669 554.223 c
h
S
Q
q
0.4 w
307.05 519.938 m
307.05 520.766 306.378 521.438 305.55 521.438 c
304.721 521.438 304.05 520.766 304.05 519.938 c
304.05 519.109 304.721 518.438 305.55 518.438 c
306.378 518.438 307.05 519.109 307.05 519.938 c
h
f*
307.05 519.938 m
307.05 520.766 306.378 521.438 305.55 521.438 c
304.721 521.438 304.05 520.766 304.05 519.938 c
304.05 519.109 304.721 518.438 305.55 518.438 c
306.378 518.438 307.05 519.109 307.05 519.938 c
h
S
Q
q
[1 3] 0 d
0.4 w
256.487 588.355 m
323.455 506.223 l
S
Q
q
[1 3] 0 d
0.4 w
256.487 588.355 m
356.979 578.604 l
S
Q
q
[1 3] 0 d
0.4 w
256.487 588.355 m
349.741 534.794 l
S
Q
q
0.4 w
271.622 516.509 m
271.622 517.337 270.95 518.009 270.122 518.009 c
269.294 518.009 268.622 517.337 268.622 516.509 c
268.622 515.681 269.294 515.009 270.122 515.009 c
270.95 515.009 271.622 515.681 271.622 516.509 c
h
f*
271.622 516.509 m
271.622 517.337 270.95 518.009 270.122 518.009 c
269.294 518.009 268.622 517.337 268.622 516.509 c
268.622 515.681 269.294 515.009 270.122 515.009 c
270.95 515.009 271.622 515.681 271.622 516.509 c
h
S
Q
q
1.2 w
329.931 585.08 m
356.979 578.604 l
349.741 534.794 l
323.455 506.223 l
305.55 519.937 l
329.931 585.08 l
h
S
Q
q
[1 0 0 1 325.453 491.52] cm
[1 0 0 1 0 2.325] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F7_0 9.963 Tf
(b) 4.27413 Tj
4.276 -1.495 Td
/F10_0 6.974 Tf
(i) 2.8175 Tj
7.094 -1.495 Td
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@endspecial 266 x(Figure)30 b(4:)42 b(The)31 b(empt)n(y)g(p)r(en)n
(tagons)e(constructed)h(in)h(the)g(pro)r(ofs)f(of)h(Observ)-5
b(ations)29 b(3)h(\(left\))330 2534 y(and)d(4)h(\(righ)n(t\).)330
2726 y(Observ)-5 b(ation)27 b(2)i(on)f(this)h(p)r(en)n(tagon)f(and)h
(on)f Fm(d)p Fn(.)41 b(It)29 b(implies)g(the)g(existence)g(of)g(a)f
(6-hole)g(|)g(a)330 2826 y(con)n(tradiction.)36 b Ff(2)455
3010 y Fn(Let)i Fm(i)k Fj(2)g(f)p Fn(1)p Fm(;)14 b(:)g(:)g(:)e(;)i
(\014)t Fj(g)p Fn(.)71 b(If)39 b Fm(c)1366 3022 y Fe(i)1432
3010 y Fn(is)g(de\014ned,)j(then)d(w)n(e)g(de\014ne)g
Fm(S)2486 3022 y Fe(i)2555 3010 y Fn(:=)i Fm(S)5 b Fn(\()p
Fm(b)2808 3022 y Fe(i)2835 3010 y Fm(;)14 b(c)2908 3022
y Fe(i)2936 3010 y Fm(;)g(b)3009 3022 y Fe(i)p Fg(+1)3120
3010 y Fn(\))39 b(\(see)330 3110 y(Figure)e(5\).)69 b(Otherwise)37
b Fm(c)1207 3122 y Fe(i)p Fb(\000)p Fg(1)1319 3110 y
Fm(;)14 b(c)1392 3122 y Fe(i)p Fg(+1)1542 3110 y Fn(are)37
b(de\014ned)h(according)f(to)h(Observ)-5 b(ation)36 b(3,)41
b(and)c(w)n(e)772 4548 y @beginspecial 180 @llx 480 @lly
434 @urx 639 @ury 2540 @rwi @setspecial
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cleartomark
%%EndResource
/F4_0 /MZHZCY+CMMI10 1 1
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pdfMakeFont
%%BeginResource: font RRHLLU+CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
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/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /RRHLLU+CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 105 /i put
dup 106 /j put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F7_0 /RRHLLU+CMMI7 1 1
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pdfMakeFont
%%BeginResource: font RNYNXW+CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /RNYNXW+CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 43 /plus put
dup 49 /one put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F10_0 /RNYNXW+CMR7 1 1
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0.4 w
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S
Q
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226.669 582.834 m
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223.669 582.006 224.341 581.334 225.169 581.334 c
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h
f*
226.669 582.834 m
226.669 583.663 225.998 584.334 225.169 584.334 c
224.341 584.334 223.669 583.663 223.669 582.834 c
223.669 582.006 224.341 581.334 225.169 581.334 c
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h
S
Q
q
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227.912 531.59 m
227.912 532.419 227.24 533.09 226.412 533.09 c
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224.912 530.762 225.584 530.09 226.412 530.09 c
227.24 530.09 227.912 530.762 227.912 531.59 c
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f*
227.912 531.59 m
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225.584 533.09 224.912 532.419 224.912 531.59 c
224.912 530.762 225.584 530.09 226.412 530.09 c
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270.487 481.368 271.158 482.039 271.158 482.868 c
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f*
271.158 482.868 m
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Q
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308.761 607.556 m
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f*
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f*
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h
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Q
q
0.4 w
281.667 511.631 m
281.667 512.459 280.995 513.131 280.167 513.131 c
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278.667 510.803 279.338 510.131 280.167 510.131 c
280.995 510.131 281.667 510.803 281.667 511.631 c
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f*
281.667 511.631 m
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S
Q
q
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323.037 527.069 m
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h
f*
323.037 527.069 m
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h
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Q
q
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Q
q
0.4 w
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317.485 550.626 318.156 549.955 318.985 549.955 c
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h
f*
320.485 551.455 m
320.485 552.283 319.813 552.955 318.985 552.955 c
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319.813 549.955 320.485 550.626 320.485 551.455 c
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S
Q
q
0.4 w
397.621 605.345 m
321.36 591.639 l
S
q
321.36 591.639 m
326.576 590.883 l
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321.36 591.639 l
h
f*
321.36 591.639 m
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h
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Q
Q
q
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394.642 625.207 m
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S
q
335.86 608.747 m
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335.86 608.747 l
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335.86 608.747 m
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q
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289.164 596.201 289.836 595.53 290.664 595.53 c
291.493 595.53 292.164 596.201 292.164 597.03 c
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292.164 597.03 m
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h
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q
0.4 w
290.037 532.57 m
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289.366 531.07 290.037 531.741 290.037 532.57 c
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f*
290.037 532.57 m
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Q
q
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318.985 551.456 m
288.537 532.571 l
274.909 579.547 l
290.664 597.03 l
314.823 573.186 l
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q
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f*
276.409 579.547 m
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h
S
Q
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S
Q
q
[4] 0 d
0.4 w
256.741 557.604 m
226.412 531.59 l
S
Q
q
[4] 0 d
0.4 w
256.741 557.604 m
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S
Q
q
0.4 w
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f*
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h
S
Q
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0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
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4.276 -1.494 Td
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q
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0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
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q
0.4 w
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333.21 579.954 m
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h
S
Q
q
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0 g
0 G
[1 0 0 1 0 0] Tm
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0 0 Td
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(d) 5.18076 Tj
Q
q
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S
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[4] 0 d
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q
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0 g
0 G
[1 0 0 1 0 0] Tm
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0 0 Td
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(j) 3.2987 Tj
Q
q
[1 0 0 1 332.573 499.579] cm
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0 g
0 G
[1 0 0 1 0 0] Tm
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(+1) 10.0844 Tj
Q
q
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0 G
[1 0 0 1 0 0] Tm
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(c) 4.31398 Tj
4.311 -1.494 Td
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(j) 3.2987 Tj
8.011 -1.494 Td
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(\000) 6.22778 Tj
14.238 -1.494 Td
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(1) 3.96821 Tj
Q
q
[1 0 0 1 312.214 515.469] cm
[1 0 0 1 0 2.85] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
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(c) 4.31398 Tj
4.311 -1.494 Td
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(j) 3.2987 Tj
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Q
q
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0 G
[1 0 0 1 0 0] Tm
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28 TJm
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Q
q
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@endspecial 1065 4813 a(Figure)27 b(5:)36 b(A)28 b(3-sector)e
Fm(S)1879 4825 y Fe(i)1934 4813 y Fn(and)h(a)h(4-sector)d
Fm(R)2537 4825 y Fe(j)2572 4813 y Fn(.)330 5008 y(de\014ne)j
Fm(R)633 5020 y Fe(i)684 5008 y Fn(:=)22 b Fm(S)5 b Fn(\()p
Fm(b)918 5020 y Fe(i)946 5008 y Fm(;)14 b(c)1019 5020
y Fe(i)p Fb(\000)p Fg(1)1131 5008 y Fm(;)g(c)1204 5020
y Fe(i)p Fg(+1)1316 5008 y Fm(;)g(b)1389 5020 y Fe(i)p
Fg(+1)1500 5008 y Fn(\).)455 5108 y(Observ)n(e)36 b(that)j(the)f
(exterior)f(of)h(con)n(v)p Fm(B)43 b Fn(is)38 b(co)n(v)n(ered)e(b)n(y)i
(the)h(3-sectors)d Fm(S)5 b Fn(\()p Fm(b)2983 5120 y
Fe(i)3010 5108 y Fm(;)14 b(d;)g(b)3163 5120 y Fe(i)p
Fg(+1)3275 5108 y Fn(\),)330 5207 y Fm(i)41 b Fn(=)f(1)p
Fm(;)14 b(:)g(:)g(:)f(;)h(\014)t Fn(.)70 b(Eac)n(h)37
b Fm(S)5 b Fn(\()p Fm(b)1216 5219 y Fe(i)1243 5207 y
Fm(;)14 b(d;)g(b)1396 5219 y Fe(i)p Fg(+1)1508 5207 y
Fn(\))38 b(is)h(co)n(v)n(ered)d(either)i(b)n(y)g Fm(S)2404
5219 y Fe(i)2470 5207 y Fn(\(if)i Fm(S)2641 5219 y Fe(i)2707
5207 y Fn(is)e(de\014ned\))h(or)e(b)n(y)330 5307 y Fm(S)381
5319 y Fe(i)p Fb(\000)p Fg(1)504 5307 y Fj([)10 b Fm(R)632
5319 y Fe(i)670 5307 y Fj([)g Fm(S)786 5319 y Fe(i)p
Fg(+1)921 5307 y Fn(\(otherwise\).)35 b(Th)n(us,)24 b(the)g
Fm(\014)k Fn(sectors)22 b Fm(S)2150 5319 y Fe(i)2201
5307 y Fn(and)h Fm(R)2421 5319 y Fe(i)2472 5307 y Fn(co)n(v)n(er)f(the)
i(en)n(tire)e(exterior)330 5407 y(of)31 b(con)n(v)p Fm(B)t
Fn(.)49 b(In)31 b(particular,)g(eac)n(h)g(p)r(oin)n(t)g(of)g
Fm(A)h Fn(lies)f(in)h(at)f(least)g(one)g(of)g(them.)49
b(In)31 b(fact,)i(the)330 5506 y Fm(R)393 5518 y Fe(i)421
5506 y Fn('s)27 b(con)n(tain)g(no)g(p)r(oin)n(ts)h(of)f
Fm(A)p Fn(:)330 5670 y Fk(Observ)-5 b(ation)31 b(4)42
b Fl(Each)31 b Fm(R)1225 5682 y Fe(i)1282 5670 y Fl(c)l(ontains)f(no)g
(p)l(oint)g(of)g Fm(A)p Fl(.)1809 5919 y Fn(4)p eop end
%%Page: 5 5
TeXDict begin 5 4 bop 330 390 a Fl(Pr)l(o)l(of.)85 b
Fn(Supp)r(ose)27 b(a)g(p)r(oin)n(t)g Fm(a)c Fj(2)g Fm(A)k
Fn(lies)g(in)g Fm(R)1778 402 y Fe(i)1806 390 y Fn(.)36
b(A)27 b(unique)g(edge)g Fm(cc)2484 360 y Fb(0)2534 390
y Fn(of)f(con)n(v)q Fm(C)33 b Fn(in)n(tersects)26 b Fm(T)3303
402 y Fe(i)330 490 y Fn(\(p)r(ossibly)j Fm(c)d Fn(=)g
Fm(c)872 502 y Fe(i)p Fb(\000)p Fg(1)1014 490 y Fn(and/or)i
Fm(c)1329 460 y Fb(0)1378 490 y Fn(=)e Fm(c)1505 502
y Fe(i)p Fg(+1)1617 490 y Fn(\).)42 b(The)30 b(con)n(v)n(ex)e(p)r(en)n
(tagon)g Fm(cb)2594 502 y Fe(i)2622 490 y Fm(ab)2702
502 y Fe(i)p Fg(+1)2813 490 y Fm(c)2849 460 y Fb(0)2902
490 y Fn(is)h(empt)n(y)g(b)n(y)330 589 y(Observ)-5 b(ation)20
b(1)g(\(see)h(the)h(righ)n(t)e(picture)h(in)h(Figure)e(4\).)35
b(This)21 b(p)r(en)n(tagon)f(and)h(the)g(p)r(oin)n(t)g
Fm(d)h Fn(sat-)330 689 y(isfy)g(the)g(assumptions)e(of)i(Observ)-5
b(ation)20 b(2.)34 b(Th)n(us,)23 b Fm(P)33 b Fn(con)n(tains)21
b(a)g(6-hole)g(|)g(a)g(con)n(tradiction.)330 789 y Ff(2)455
979 y Fn(Th)n(us,)42 b(all)d(p)r(oin)n(ts)g(of)h Fm(A)g
Fn(lie)f(in)h(the)g(union)g(of)f(the)h Fm(S)2241 991
y Fe(i)2268 979 y Fn('s.)73 b(Let)40 b Fm(t)i Fj(\025)h
Fn(1.)72 b(Whenev)n(er)39 b Fm(t)330 1078 y Fn(consecutiv)n(e)23
b(3-sectors)e Fm(S)1154 1090 y Fe(i)1182 1078 y Fm(;)14
b(S)1270 1090 y Fe(i)p Fg(+1)1381 1078 y Fm(;)g(:)g(:)g(:)g(;)g(S)1617
1090 y Fe(i)p Fg(+)p Fe(t)p Fb(\000)p Fg(1)1829 1078
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Fm(S)3235 1090 y Fe(i;t)3307 1078 y Fn(:)1263 1249 y
Fm(S)1314 1261 y Fe(i;t)1409 1249 y Fn(:=)f Fm(S)1571
1261 y Fe(i)1617 1249 y Fj([)c Fm(S)1742 1261 y Fe(i)p
Fg(+1)1872 1249 y Fj([)g(\001)14 b(\001)g(\001)k([)h
Fm(S)2186 1261 y Fe(i)p Fg(+)p Fe(t)p Fb(\000)p Fg(1)2374
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Fl(p)l(oints)g(of)h Fm(A)p Fl(.)330 1862 y(Pr)l(o)l(of.)85
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Fm(t)p Fn(.)37 b(Without)27 b(loss)e(of)i(generalit)n(y)-7
b(,)25 b(w)n(e)h(supp)r(ose)g(that)330 1962 y Fm(i)d
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h Fm(A)27 b Fj(\\)g Fm(S)2243 2173 y Fg(1)2321 2161 y
Fn(form)40 b(a)g(6-hole)g(according)e(to)330 2260 y(Observ)-5
b(ation)26 b(1.)455 2360 y(Supp)r(ose)j(no)n(w)g(that)h
Fm(t)c(>)f Fn(1)k(and)h(that)f(the)h(lemma)f(holds)g(for)g
Fm(t)20 b Fj(\000)f Fn(1.)42 b(W)-7 b(e)30 b(partition)f
Fm(S)3248 2372 y Fg(1)p Fe(;t)330 2460 y Fn(in)n(to)22
b Fm(S)544 2472 y Fg(2)p Fe(;t)p Fb(\000)p Fg(1)734 2460
y Fn(and)g Fm(W)35 b Fn(:=)23 b Fm(S)1165 2472 y Fg(1)p
Fe(;t)1255 2460 y Fj(n)8 b Fm(S)1356 2472 y Fg(2)p Fe(;t)p
Fb(\000)p Fg(1)1545 2460 y Fn(\(see)23 b(the)f(left)i(picture)e(in)h
(Figure)f(6\).)35 b(Note)22 b(that)h Fm(S)3163 2472 y
Fg(2)p Fe(;t)p Fb(\000)p Fg(1)330 3628 y @beginspecial
45 @llx 438 @lly 413 @urx 563 @ury 3680 @rwi @setspecial
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% PDF special state
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/pdfSetup {
3 1 roll 2 array astore
/setpagedevice where {
pop 3 dict begin
/PageSize exch def
/ImagingBBox null def
/Policies 1 dict dup begin /PageSize 3 def end def
{ /Duplex true def } if
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} {
pop pop
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} def
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pdfDictSize dict begin
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/pdfCharSpacing 0 def
/pdfTextRender 0 def
/pdfTextRise 0 def
/pdfWordSpacing 0 def
/pdfHorizScaling 1 def
} def
/pdfEndPage { end } def
% separation convention operators
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pop
}{
/findcmykcustomcolor { 5 array astore } def
} ifelse
/setcustomcolor where {
pop
}{
/setcustomcolor {
exch
[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
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[ exch /dup load exch { mul exch dup } /forall load
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pop
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gsave
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10 dict begin
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currentdict end
image
grestore
} def
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pdfLastStroke not {
pdfStroke aload length
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pop setgray
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4 eq {
setcmykcolor
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setcmykcolor
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4 2 roll matrix scale makefont
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currentdict
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definefont pop
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currentdict
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definefont pop
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false
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exch 1 array astore composefont pop
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pdfMakeFont16
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/cm { concat } def
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/i { setflat } def
/j { setlinejoin } def
/J { setlinecap } def
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/G { dup 1 array astore /pdfStroke exch def setgray
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findcmykcustomcolor exch setcustomcolor
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/CK { 6 copy 6 array astore /pdfStroke exch def
findcmykcustomcolor exch setcustomcolor
/pdfLastStroke true def /pdfLastFill false def } def
% path segment operators
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/l { lineto } def
/c { curveto } def
/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
neg 0 rlineto closepath } def
/h { closepath } def
% path painting operators
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/f { fCol fill } def
/f* { fCol eofill } def
% clipping operators
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/W* { eoclip newpath } def
% text state operators
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/Tf { dup /pdfFontSize exch def
dup pdfHorizScaling mul exch matrix scale
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/Ts { /pdfTextRise exch def } def
/Tw { /pdfWordSpacing exch def } def
/Tz { /pdfHorizScaling exch def } def
% text positioning operators
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/Tm { /pdfTextMat exch def } def
% text string operators
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3 index 3 index rmoveto
4 index eq { 5 index 5 index rmoveto } if
} forall
6 {pop} repeat
} def
/Tj { fCol
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pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32
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pdfTextMat dtransform
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pdfTextRender 1 and 0 eq {
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0 pdfTextRise pdfTextMat dtransform rmoveto
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sub exch div
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pdfTextMat dtransform
6 5 roll awidthshow
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pdfTextMat dtransform
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0 pdfTextRise neg pdfTextMat dtransform rmoveto } def
/TJm { pdfFontSize 0.001 mul mul neg 0
pdfTextMat dtransform rmoveto } def
/TJmV { pdfFontSize 0.001 mul mul neg 0 exch
pdfTextMat dtransform rmoveto } def
% Level 1 image operators
/pdfIm1 {
/pdfImBuf1 4 index string def
{ currentfile pdfImBuf1 readhexstring pop } image
} def
/pdfIm1Sep {
/pdfImBuf1 4 index string def
/pdfImBuf2 4 index string def
/pdfImBuf3 4 index string def
/pdfImBuf4 4 index string def
{ currentfile pdfImBuf1 readhexstring pop }
{ currentfile pdfImBuf2 readhexstring pop }
{ currentfile pdfImBuf3 readhexstring pop }
{ currentfile pdfImBuf4 readhexstring pop }
true 4 colorimage
} def
/pdfImM1 {
/pdfImBuf1 4 index 7 add 8 idiv string def
{ currentfile pdfImBuf1 readhexstring pop } imagemask
} def
% Level 2 image operators
/pdfImBuf 100 string def
/pdfIm {
image
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
/pdfImSep {
findcmykcustomcolor exch
dup /Width get /pdfImBuf1 exch string def
begin Width Height BitsPerComponent ImageMatrix DataSource end
/pdfImData exch def
{ pdfImData pdfImBuf1 readstring pop
0 1 2 index length 1 sub {
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6 5 roll customcolorimage
{ currentfile pdfImBuf readline
not { pop exit } if
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} def
/pdfImM {
fCol imagemask
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} def
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%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
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0 1 255 {1 index exch /.notdef put} for
dup 43 /plus put
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dup 51 /three put
dup 52 /four put
dup 53 /five put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
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currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F7_0 /NGFEGD+CMR7 1 1
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pdfMakeFont
%%BeginResource: font CWOSIR+CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CWOSIR+CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 61 /equal put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F10_0 /CWOSIR+CMR10 1 1
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pdfMakeFont
%%BeginResource: font UCXRUA+CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /UCXRUA+CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /beta put
dup 59 /comma put
dup 116 /t put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F13_0 /UCXRUA+CMMI7 1 1
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153.504 458.603 m
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S
Q
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1.2 w
166.763 452.649 m
197.258 438.953 l
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Q
q
1.2 w
166.763 452.649 m
156.953 478.417 l
134.125 502.529 l
112.289 513.862 l
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S
Q
q
0.4 w
112.289 513.862 m
129.552 532.868 l
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Q
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0.4 w
134.125 502.529 m
126.25 533.613 l
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Q
q
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134.125 502.529 m
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0 G
[1 0 0 1 0 0] Tm
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0 0 Td
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0 G
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4.276 -1.494 Td
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11.512 0 Td
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(b) 4.27413 Tj
26.304 -1.494 Td
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0 G
[1 0 0 1 0 0] Tm
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21.683 -1.494 Td
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(1) 3.96821 Tj
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q
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0 g
0 G
[1 0 0 1 0 0] Tm
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0 0 Td
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(b) 4.27413 Tj
4.276 -1.494 Td
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Q
q
[1 0 0 1 75.1493 500.102] cm
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0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
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(b) 4.27413 Tj
4.276 -1.494 Td
/F7_0 6.974 Tf
(1) 3.96821 Tj
Q
q
[1 0 0 1 94.613 491.468] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(c) 4.31398 Tj
4.311 -1.494 Td
/F7_0 6.974 Tf
(1) 3.96821 Tj
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0.4 w
84.6392 511.303 m
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81.6392 510.475 82.3108 509.803 83.1392 509.803 c
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h
f*
84.6392 511.303 m
84.6392 512.132 83.9677 512.803 83.1392 512.803 c
82.3108 512.803 81.6392 512.132 81.6392 511.303 c
81.6392 510.475 82.3108 509.803 83.1392 509.803 c
83.9677 509.803 84.6392 510.475 84.6392 511.303 c
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S
Q
q
0.4 w
113.789 513.862 m
113.789 514.691 113.117 515.362 112.289 515.362 c
111.461 515.362 110.789 514.691 110.789 513.862 c
110.789 513.034 111.461 512.362 112.289 512.362 c
113.117 512.362 113.789 513.034 113.789 513.862 c
h
f*
113.789 513.862 m
113.789 514.691 113.117 515.362 112.289 515.362 c
111.461 515.362 110.789 514.691 110.789 513.862 c
110.789 513.034 111.461 512.362 112.289 512.362 c
113.117 512.362 113.789 513.034 113.789 513.862 c
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Q
q
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102.488 501.421 m
102.488 502.249 101.816 502.921 100.988 502.921 c
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99.488 500.592 100.16 499.921 100.988 499.921 c
101.816 499.921 102.488 500.592 102.488 501.421 c
h
f*
102.488 501.421 m
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100.16 502.921 99.488 502.249 99.488 501.421 c
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101.816 499.921 102.488 500.592 102.488 501.421 c
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Q
q
0.4 w
121.546 494.86 m
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118.546 494.032 119.218 493.36 120.046 493.36 c
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f*
121.546 494.86 m
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1.2 w
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[4] 0 d
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100.988 501.421 m
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0 G
[1 0 0 1 0 0] Tm
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Q
q
0.4 w
Q
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0 G
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4.311 -1.494 Td
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11.548 0 Td
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(=) 7.75121 Tj
22.064 0 Td
/F4_0 9.963 Tf
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26.376 -1.494 Td
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(t) 3.01277 Tj
Q
q
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0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(c) 4.31398 Tj
4.311 -1.494 Td
/F7_0 6.974 Tf
(2) 3.96821 Tj
Q
q
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293.219 501.52 292.547 502.191 291.719 502.191 c
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290.219 499.863 290.89 499.191 291.719 499.191 c
292.547 499.191 293.219 499.863 293.219 500.691 c
h
f*
293.219 500.691 m
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290.89 502.191 290.219 501.52 290.219 500.691 c
290.219 499.863 290.89 499.191 291.719 499.191 c
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h
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0.4 w
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371.791 452.904 371.119 453.575 370.291 453.575 c
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368.791 451.247 369.462 450.575 370.291 450.575 c
371.119 450.575 371.791 451.247 371.791 452.075 c
h
f*
371.791 452.075 m
371.791 452.904 371.119 453.575 370.291 453.575 c
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368.791 451.247 369.462 450.575 370.291 450.575 c
371.119 450.575 371.791 451.247 371.791 452.075 c
h
S
Q
q
0.4 w
0.875 g
310.104 544.238 m
298.869 517.627 l
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318.602 543.254 l
310.104 544.238 l
h
f*
Q
q
0.4 w
0.875 g
342.848 536.512 m
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349.855 508.853 l
342.848 536.512 l
h
f*
Q
q
0.4 w
0.875 g
349.855 508.853 m
372.683 484.741 l
377.857 514.463 l
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349.855 508.853 l
h
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Q
q
0.4 w
0.875 g
372.683 484.741 m
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402.858 470.485 l
399.052 479.659 l
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h
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q
1.2 w
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1.2 w
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0.4 w
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0.4 w
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S
Q
q
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0.4 w
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S
Q
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297.369 516.799 298.04 516.127 298.869 516.127 c
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h
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300.369 517.627 m
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328.847 518.686 329.519 519.358 329.519 520.186 c
h
f*
329.519 520.186 m
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326.519 519.358 327.19 518.686 328.019 518.686 c
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h
S
Q
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0.4 w
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348.355 508.025 349.026 507.353 349.855 507.353 c
350.683 507.353 351.355 508.025 351.355 508.853 c
h
f*
351.355 508.853 m
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349.026 510.353 348.355 509.682 348.355 508.853 c
348.355 508.025 349.026 507.353 349.855 507.353 c
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S
Q
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374.183 484.741 m
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371.183 483.913 371.854 483.241 372.683 483.241 c
373.511 483.241 374.183 483.913 374.183 484.741 c
h
f*
374.183 484.741 m
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371.183 483.913 371.854 483.241 372.683 483.241 c
373.511 483.241 374.183 483.913 374.183 484.741 c
h
S
Q
q
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383.993 458.973 m
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381.664 460.473 380.993 459.802 380.993 458.973 c
380.993 458.145 381.664 457.473 382.493 457.473 c
383.321 457.473 383.993 458.145 383.993 458.973 c
h
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383.993 458.973 m
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383.321 457.473 383.993 458.145 383.993 458.973 c
h
S
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q
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[1 0 0 1 0 2.473] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
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(S) 6.10732 Tj
6.683 3.615 Td
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(0) 2.29445 Tj
6.109 -2.473 Td
/F7_0 6.974 Tf
(1) 3.96821 Tj
Q
q
[1 0 0 1 334.959 517.811] cm
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0 g
0 G
[1 0 0 1 0 0] Tm
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6.683 3.615 Td
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(0) 2.29445 Tj
6.109 -2.473 Td
/F7_0 6.974 Tf
(2) 3.96821 Tj
Q
q
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0 g
0 G
[1 0 0 1 0 0] Tm
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6.683 3.615 Td
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(0) 2.29445 Tj
6.109 -2.473 Td
/F7_0 6.974 Tf
(3) 3.96821 Tj
Q
q
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[1 0 0 1 0 2.473] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
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(S) 6.10732 Tj
6.683 3.615 Td
/F16_0 6.974 Tf
(0) 2.29445 Tj
6.109 -2.473 Td
/F7_0 6.974 Tf
(4) 3.96821 Tj
Q
q
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0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
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(c) 4.31398 Tj
4.311 -1.494 Td
/F7_0 6.974 Tf
(5) 3.96821 Tj
Q
q
[1 0 0 1 286.311 489.108] cm
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0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
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/F4_0 9.963 Tf
(c) 4.31398 Tj
4.311 -1.494 Td
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@endspecial 266 x Fn(Figure)29 b(6:)39 b(The)30 b(partition)f(of)g
Fm(S)1366 3906 y Fg(1)p Fe(;t)1477 3894 y Fn(in)n(to)g
Fm(S)1698 3906 y Fg(2)p Fe(;t)p Fb(\000)p Fg(1)1894 3894
y Fn(and)h Fm(W)41 b Fn(\(left\))30 b(and)g(four)e(of)i(the)f(regions)f
Fm(S)3307 3864 y Fb(0)3302 3916 y Fe(i)330 3994 y Fn(\(righ)n(t\).)330
4185 y(con)n(tains)f(at)g(most)h Fm(t)f Fn(p)r(oin)n(ts)h(b)n(y)f(the)h
(inductiv)n(e)g(assumption.)455 4285 y(Supp)r(ose)39
b(that)h(the)h(quadrilateral)c Fm(Q)43 b Fn(:=)g Fm(b)1919
4297 y Fg(1)1956 4285 y Fm(c)1992 4297 y Fg(1)2029 4285
y Fm(c)2065 4297 y Fg(2)2103 4285 y Fm(b)2139 4297 y
Fg(2)2215 4285 y Fn(is)d(con)n(v)n(ex.)72 b(Then)40 b
Fm(W)52 b Fn(do)r(es)39 b(not)330 4385 y(con)n(tain)28
b(t)n(w)n(o)g(di\013eren)n(t)h(p)r(oin)n(ts)f Fm(a;)14
b(a)1486 4354 y Fb(0)1534 4385 y Fj(2)25 b Fm(A)p Fn(,)30
b(since)e(otherwise)g(the)h(5-hole)e Fm(c)2729 4397 y
Fg(1)2767 4385 y Fm(b)2803 4397 y Fg(1)2839 4385 y Fm(aa)2927
4354 y Fb(0)2951 4385 y Fm(b)2987 4397 y Fg(2)3052 4385
y Fn(and)i(the)330 4484 y(p)r(oin)n(t)36 b Fm(c)591 4496
y Fg(2)664 4484 y Fn(satisfy)f(the)h(assumptions)g(of)f(Observ)-5
b(ation)35 b(2.)61 b(Therefore)34 b Fm(S)2699 4496 y
Fg(1)p Fe(;t)2818 4484 y Fn(=)i Fm(W)g Fj([)24 b Fm(S)3163
4496 y Fg(2)p Fe(;t)p Fb(\000)p Fg(1)330 4584 y Fn(con)n(tains)j(at)g
(most)h(1)17 b(+)h Fm(t)28 b Fn(p)r(oin)n(ts)g(of)f Fm(A)h
Fn(in)g(this)g(case.)455 4683 y(Th)n(us,)d(w)n(e)g(ma)n(y)g(supp)r(ose)
g(that)g(the)h(quadrilateral)d Fm(Q)i Fn(is)h(non-con)n(v)n(ex.)34
b(This)25 b(means)g(that)330 4783 y(the)36 b(p)r(oin)n(t)f
Fm(c)741 4795 y Fg(1)814 4783 y Fn(lies)g(inside)h(the)g(triangle)e
Fm(b)1708 4795 y Fg(1)1745 4783 y Fm(b)1781 4795 y Fg(2)1818
4783 y Fm(c)1854 4795 y Fg(2)1891 4783 y Fn(.)61 b(Analogously)34
b(w)n(e)h(ma)n(y)f(supp)r(ose)i(on)f(the)330 4883 y(\\opp)r(osite")d
(side)i(of)g Fm(S)1074 4895 y Fg(1)p Fe(;t)1190 4883
y Fn(that)g(the)g(p)r(oin)n(t)g Fm(c)1784 4895 y Fe(t)1847
4883 y Fn(lies)g(inside)f(the)i(triangle)d Fm(b)2734
4895 y Fe(t)2763 4883 y Fm(b)2799 4895 y Fe(t)p Fg(+1)2912
4883 y Fm(c)2948 4895 y Fe(t)p Fb(\000)p Fg(1)3062 4883
y Fn(.)56 b(Then)330 4982 y(the)31 b(p)r(olygon)f Fm(H)35
b Fn(:=)28 b Fm(b)1049 4994 y Fg(1)1086 4982 y Fm(c)1122
4994 y Fg(1)1159 4982 y Fm(c)1195 4994 y Fg(2)1246 4982
y Fm(:)14 b(:)g(:)g(c)1393 4994 y Fe(t)1422 4982 y Fm(b)1458
4994 y Fe(t)p Fg(+1)1602 4982 y Fn(is)30 b(con)n(v)n(ex.)45
b(Let)31 b Fm(A)2216 4952 y Fb(0)2271 4982 y Fn(b)r(e)g(the)g(set)g(in)
g(con)n(v)n(ex)e(p)r(osition)330 5082 y(obtained)36 b(from)g
Fm(A)h Fn(b)n(y)f(replacing)f(the)i(p)r(oin)n(ts)f(of)h
Fm(A)24 b Fj(\\)h Fm(S)2203 5094 y Fg(1)p Fe(;t)2321
5082 y Fn(b)n(y)37 b(the)f Fm(t)25 b Fn(+)f(2)36 b(v)n(ertices)f(of)h
Fm(H)7 b Fn(.)330 5182 y(Observ)n(e)25 b(that)h Fm(S)877
5194 y Fg(1)p Fe(;t)982 5182 y Fn(=)d Fm(S)1121 5194
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pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32
4 3 roll pdfCharSpacing pdfHorizScaling mul add 0
pdfTextMat dtransform
6 5 roll awidthshow
0 pdfTextRise neg pdfTextMat dtransform rmoveto } def
/Tj16V { pdfTextRender 1 and 0 eq { fCol } { sCol } ifelse
0 pdfTextRise pdfTextMat dtransform rmoveto
2 index stringwidth pdfTextMat idtransform exch pop
sub exch div
0 pdfWordSpacing pdfTextMat dtransform 32
4 3 roll pdfCharSpacing add 0 exch
pdfTextMat dtransform
6 5 roll awidthshow
0 pdfTextRise neg pdfTextMat dtransform rmoveto } def
/TJm { pdfFontSize 0.001 mul mul neg 0
pdfTextMat dtransform rmoveto } def
/TJmV { pdfFontSize 0.001 mul mul neg 0 exch
pdfTextMat dtransform rmoveto } def
% Level 1 image operators
/pdfIm1 {
/pdfImBuf1 4 index string def
{ currentfile pdfImBuf1 readhexstring pop } image
} def
/pdfIm1Sep {
/pdfImBuf1 4 index string def
/pdfImBuf2 4 index string def
/pdfImBuf3 4 index string def
/pdfImBuf4 4 index string def
{ currentfile pdfImBuf1 readhexstring pop }
{ currentfile pdfImBuf2 readhexstring pop }
{ currentfile pdfImBuf3 readhexstring pop }
{ currentfile pdfImBuf4 readhexstring pop }
true 4 colorimage
} def
/pdfImM1 {
/pdfImBuf1 4 index 7 add 8 idiv string def
{ currentfile pdfImBuf1 readhexstring pop } imagemask
} def
% Level 2 image operators
/pdfImBuf 100 string def
/pdfIm {
image
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
/pdfImSep {
findcmykcustomcolor exch
dup /Width get /pdfImBuf1 exch string def
begin Width Height BitsPerComponent ImageMatrix DataSource end
/pdfImData exch def
{ pdfImData pdfImBuf1 readstring pop
0 1 2 index length 1 sub {
1 index exch 2 copy get 255 exch sub put
} for }
6 5 roll customcolorimage
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
/pdfImM {
fCol imagemask
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
end
%%EndResource
%%EndProlog
%%BeginSetup
xpdf begin
%%BeginResource: font XYQGXL+CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /XYQGXL+CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 66 /B put
dup 71 /G put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
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pdfMakeFont
%%BeginResource: font PAIOSN+CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /PAIOSN+CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font IHPULD+CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /IHPULD+CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 61 /equal put
dup 99 /c put
dup 110 /n put
dup 111 /o put
dup 118 /v put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F10_0 /IHPULD+CMR10 1 1
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font ACEJPC+CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /ACEJPC+CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /beta put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F13_0 /ACEJPC+CMMI7 1 1
[ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
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pdfMakeFont
%%EndSetup
%
%
%
%
%
%299.673 565.521 m
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%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%$c_8$
%
%
%
%
%
%
%
%
%
%
%$a_1$
%$a_2$
%$a_3$
%$a_4$
%$a_5$
%$a_6$
%$a_7$
%$a_8$
%$a_9=a_\beta$
%$a$
%
%271.954 580.717 m
%299.674 565.521 l
%323.311 541.068 l
%314.345 492.978 l
%284.187 449.778 l
%254.843 447.332 l
%218.142 449.543 l
%198.19 511.422 l
%213.515 550.169 l
%236.069 568.964 l h
%
%
%323.311 541.068 m
%349.394 519.061 l
%353.47 481.566 l
%329.017 456.298 l
%284.187 449.778 l h
%
%$G$
%$b_4$
%$b_5$
%$b_6$
%$b_3$
%$b_2$
%$b_1$
%$d$
%$c_1$
%$c_2$
%$c_3$
%$c_4$
%$c_5$
%$c_6$
%$c_7$
%$c_9=c_\beta$
%
%420.454 487.217 m
%367.826 493.231 l
%
%${\rm conv}B$
%$b_7$
%
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[] 0 d
0 i
0 j
0 J
10 M
1 w
0 g
0 G
173.322 405.013 281.252 188.952 re
W
q
q
0.4 w
299.673 565.521 m
355.1 546.774 l
372.217 505.204 l
354.284 456.298 l
311.084 438.366 l
254.843 447.333 l
221.424 486.457 l
228.76 525.582 l
253.213 553.295 l
299.673 565.521 l
h
S
Q
q
0.4 w
301.173 565.521 m
301.173 566.35 300.501 567.021 299.673 567.021 c
298.845 567.021 298.173 566.35 298.173 565.521 c
298.173 564.693 298.845 564.021 299.673 564.021 c
300.501 564.021 301.173 564.693 301.173 565.521 c
h
f*
301.173 565.521 m
301.173 566.35 300.501 567.021 299.673 567.021 c
298.845 567.021 298.173 566.35 298.173 565.521 c
298.173 564.693 298.845 564.021 299.673 564.021 c
300.501 564.021 301.173 564.693 301.173 565.521 c
h
S
Q
q
0.4 w
356.6 546.774 m
356.6 547.603 355.928 548.274 355.1 548.274 c
354.271 548.274 353.6 547.603 353.6 546.774 c
353.6 545.946 354.271 545.274 355.1 545.274 c
355.928 545.274 356.6 545.946 356.6 546.774 c
h
f*
356.6 546.774 m
356.6 547.603 355.928 548.274 355.1 548.274 c
354.271 548.274 353.6 547.603 353.6 546.774 c
353.6 545.946 354.271 545.274 355.1 545.274 c
355.928 545.274 356.6 545.946 356.6 546.774 c
h
S
Q
q
0.4 w
373.717 505.204 m
373.717 506.033 373.045 506.704 372.217 506.704 c
371.388 506.704 370.717 506.033 370.717 505.204 c
370.717 504.376 371.388 503.704 372.217 503.704 c
373.045 503.704 373.717 504.376 373.717 505.204 c
h
f*
373.717 505.204 m
373.717 506.033 373.045 506.704 372.217 506.704 c
371.388 506.704 370.717 506.033 370.717 505.204 c
370.717 504.376 371.388 503.704 372.217 503.704 c
373.045 503.704 373.717 504.376 373.717 505.204 c
h
S
Q
q
0.4 w
355.784 456.298 m
355.784 457.127 355.113 457.798 354.284 457.798 c
353.456 457.798 352.784 457.127 352.784 456.298 c
352.784 455.47 353.456 454.798 354.284 454.798 c
355.113 454.798 355.784 455.47 355.784 456.298 c
h
f*
355.784 456.298 m
355.784 457.127 355.113 457.798 354.284 457.798 c
353.456 457.798 352.784 457.127 352.784 456.298 c
352.784 455.47 353.456 454.798 354.284 454.798 c
355.113 454.798 355.784 455.47 355.784 456.298 c
h
S
Q
q
0.4 w
312.584 438.366 m
312.584 439.195 311.913 439.866 311.084 439.866 c
310.256 439.866 309.584 439.195 309.584 438.366 c
309.584 437.538 310.256 436.866 311.084 436.866 c
311.913 436.866 312.584 437.538 312.584 438.366 c
h
f*
312.584 438.366 m
312.584 439.195 311.913 439.866 311.084 439.866 c
310.256 439.866 309.584 439.195 309.584 438.366 c
309.584 437.538 310.256 436.866 311.084 436.866 c
311.913 436.866 312.584 437.538 312.584 438.366 c
h
S
Q
q
0.4 w
256.343 447.333 m
256.343 448.161 255.671 448.833 254.843 448.833 c
254.014 448.833 253.343 448.161 253.343 447.333 c
253.343 446.504 254.014 445.833 254.843 445.833 c
255.671 445.833 256.343 446.504 256.343 447.333 c
h
f*
256.343 447.333 m
256.343 448.161 255.671 448.833 254.843 448.833 c
254.014 448.833 253.343 448.161 253.343 447.333 c
253.343 446.504 254.014 445.833 254.843 445.833 c
255.671 445.833 256.343 446.504 256.343 447.333 c
h
S
Q
q
0.4 w
222.924 486.457 m
222.924 487.285 222.252 487.957 221.424 487.957 c
220.596 487.957 219.924 487.285 219.924 486.457 c
219.924 485.628 220.596 484.957 221.424 484.957 c
222.252 484.957 222.924 485.628 222.924 486.457 c
h
f*
222.924 486.457 m
222.924 487.285 222.252 487.957 221.424 487.957 c
220.596 487.957 219.924 487.285 219.924 486.457 c
219.924 485.628 220.596 484.957 221.424 484.957 c
222.252 484.957 222.924 485.628 222.924 486.457 c
h
S
Q
q
0.4 w
230.26 525.582 m
230.26 526.41 229.589 527.082 228.76 527.082 c
227.932 527.082 227.26 526.41 227.26 525.582 c
227.26 524.753 227.932 524.082 228.76 524.082 c
229.589 524.082 230.26 524.753 230.26 525.582 c
h
f*
230.26 525.582 m
230.26 526.41 229.589 527.082 228.76 527.082 c
227.932 527.082 227.26 526.41 227.26 525.582 c
227.26 524.753 227.932 524.082 228.76 524.082 c
229.589 524.082 230.26 524.753 230.26 525.582 c
h
S
Q
q
0.4 w
254.713 553.295 m
254.713 554.123 254.042 554.795 253.213 554.795 c
252.385 554.795 251.713 554.123 251.713 553.295 c
251.713 552.467 252.385 551.795 253.213 551.795 c
254.042 551.795 254.713 552.467 254.713 553.295 c
h
f*
254.713 553.295 m
254.713 554.123 254.042 554.795 253.213 554.795 c
252.385 554.795 251.713 554.123 251.713 553.295 c
251.713 552.467 252.385 551.795 253.213 551.795 c
254.042 551.795 254.713 552.467 254.713 553.295 c
h
S
Q
q
0.4 w
324.811 541.068 m
324.811 541.897 324.14 542.568 323.311 542.568 c
322.483 542.568 321.811 541.897 321.811 541.068 c
321.811 540.24 322.483 539.568 323.311 539.568 c
324.14 539.568 324.811 540.24 324.811 541.068 c
h
f*
324.811 541.068 m
324.811 541.897 324.14 542.568 323.311 542.568 c
322.483 542.568 321.811 541.897 321.811 541.068 c
321.811 540.24 322.483 539.568 323.311 539.568 c
324.14 539.568 324.811 540.24 324.811 541.068 c
h
S
Q
q
0.4 w
350.894 519.061 m
350.894 519.889 350.222 520.561 349.394 520.561 c
348.565 520.561 347.894 519.889 347.894 519.061 c
347.894 518.232 348.565 517.561 349.394 517.561 c
350.222 517.561 350.894 518.232 350.894 519.061 c
h
f*
350.894 519.061 m
350.894 519.889 350.222 520.561 349.394 520.561 c
348.565 520.561 347.894 519.889 347.894 519.061 c
347.894 518.232 348.565 517.561 349.394 517.561 c
350.222 517.561 350.894 518.232 350.894 519.061 c
h
S
Q
q
0.4 w
354.97 481.566 m
354.97 482.395 354.298 483.066 353.47 483.066 c
352.641 483.066 351.97 482.395 351.97 481.566 c
351.97 480.738 352.641 480.066 353.47 480.066 c
354.298 480.066 354.97 480.738 354.97 481.566 c
h
f*
354.97 481.566 m
354.97 482.395 354.298 483.066 353.47 483.066 c
352.641 483.066 351.97 482.395 351.97 481.566 c
351.97 480.738 352.641 480.066 353.47 480.066 c
354.298 480.066 354.97 480.738 354.97 481.566 c
h
S
Q
q
0.4 w
330.517 456.298 m
330.517 457.127 329.845 457.798 329.017 457.798 c
328.188 457.798 327.517 457.127 327.517 456.298 c
327.517 455.47 328.188 454.798 329.017 454.798 c
329.845 454.798 330.517 455.47 330.517 456.298 c
h
f*
330.517 456.298 m
330.517 457.127 329.845 457.798 329.017 457.798 c
328.188 457.798 327.517 457.127 327.517 456.298 c
327.517 455.47 328.188 454.798 329.017 454.798 c
329.845 454.798 330.517 455.47 330.517 456.298 c
h
S
Q
q
0.4 w
285.686 449.778 m
285.686 450.606 285.015 451.278 284.186 451.278 c
283.358 451.278 282.686 450.606 282.686 449.778 c
282.686 448.949 283.358 448.278 284.186 448.278 c
285.015 448.278 285.686 448.949 285.686 449.778 c
h
f*
285.686 449.778 m
285.686 450.606 285.015 451.278 284.186 451.278 c
283.358 451.278 282.686 450.606 282.686 449.778 c
282.686 448.949 283.358 448.278 284.186 448.278 c
285.015 448.278 285.686 448.949 285.686 449.778 c
h
S
Q
q
0.4 w
250.637 467.71 m
250.637 468.538 249.966 469.21 249.137 469.21 c
248.309 469.21 247.637 468.538 247.637 467.71 c
247.637 466.881 248.309 466.21 249.137 466.21 c
249.966 466.21 250.637 466.881 250.637 467.71 c
h
f*
250.637 467.71 m
250.637 468.538 249.966 469.21 249.137 469.21 c
248.309 469.21 247.637 468.538 247.637 467.71 c
247.637 466.881 248.309 466.21 249.137 466.21 c
249.966 466.21 250.637 466.881 250.637 467.71 c
h
S
Q
q
0.4 w
247.377 497.053 m
247.377 497.882 246.705 498.553 245.877 498.553 c
245.049 498.553 244.377 497.882 244.377 497.053 c
244.377 496.225 245.049 495.553 245.877 495.553 c
246.705 495.553 247.377 496.225 247.377 497.053 c
h
f*
247.377 497.053 m
247.377 497.882 246.705 498.553 245.877 498.553 c
245.049 498.553 244.377 497.882 244.377 497.053 c
244.377 496.225 245.049 495.553 245.877 495.553 c
246.705 495.553 247.377 496.225 247.377 497.053 c
h
S
Q
q
0.4 w
257.158 528.842 m
257.158 529.67 256.487 530.342 255.658 530.342 c
254.83 530.342 254.158 529.67 254.158 528.842 c
254.158 528.014 254.83 527.342 255.658 527.342 c
256.487 527.342 257.158 528.014 257.158 528.842 c
h
f*
257.158 528.842 m
257.158 529.67 256.487 530.342 255.658 530.342 c
254.83 530.342 254.158 529.67 254.158 528.842 c
254.158 528.014 254.83 527.342 255.658 527.342 c
256.487 527.342 257.158 528.014 257.158 528.842 c
h
S
Q
q
0.4 w
286.502 545.144 m
286.502 545.972 285.83 546.644 285.002 546.644 c
284.173 546.644 283.502 545.972 283.502 545.144 c
283.502 544.316 284.173 543.644 285.002 543.644 c
285.83 543.644 286.502 544.316 286.502 545.144 c
h
f*
286.502 545.144 m
286.502 545.972 285.83 546.644 285.002 546.644 c
284.173 546.644 283.502 545.972 283.502 545.144 c
283.502 544.316 284.173 543.644 285.002 543.644 c
285.83 543.644 286.502 544.316 286.502 545.144 c
h
S
Q
q
0.4 w
315.845 492.978 m
315.845 493.806 315.173 494.478 314.345 494.478 c
313.516 494.478 312.845 493.806 312.845 492.978 c
312.845 492.149 313.516 491.478 314.345 491.478 c
315.173 491.478 315.845 492.149 315.845 492.978 c
h
f*
315.845 492.978 m
315.845 493.806 315.173 494.478 314.345 494.478 c
313.516 494.478 312.845 493.806 312.845 492.978 c
312.845 492.149 313.516 491.478 314.345 491.478 c
315.173 491.478 315.845 492.149 315.845 492.978 c
h
S
Q
q
[1 0 0 1 231.525 494.977] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(c) 4.31398 Tj
4.311 -1.494 Td
/F7_0 6.974 Tf
(8) 3.96821 Tj
Q
q
0.4 w
273.454 580.717 m
273.454 581.546 272.782 582.217 271.954 582.217 c
271.126 582.217 270.454 581.546 270.454 580.717 c
270.454 579.889 271.126 579.217 271.954 579.217 c
272.782 579.217 273.454 579.889 273.454 580.717 c
h
f*
273.454 580.717 m
273.454 581.546 272.782 582.217 271.954 582.217 c
271.126 582.217 270.454 581.546 270.454 580.717 c
270.454 579.889 271.126 579.217 271.954 579.217 c
272.782 579.217 273.454 579.889 273.454 580.717 c
h
S
Q
q
0.4 w
354.19 579.663 m
354.19 580.491 353.518 581.163 352.69 581.163 c
351.862 581.163 351.19 580.491 351.19 579.663 c
351.19 578.835 351.862 578.163 352.69 578.163 c
353.518 578.163 354.19 578.835 354.19 579.663 c
h
f*
354.19 579.663 m
354.19 580.491 353.518 581.163 352.69 581.163 c
351.862 581.163 351.19 580.491 351.19 579.663 c
351.19 578.835 351.862 578.163 352.69 578.163 c
353.518 578.163 354.19 578.835 354.19 579.663 c
h
S
Q
q
0.4 w
396.606 538.603 m
396.606 539.431 395.934 540.103 395.106 540.103 c
394.278 540.103 393.606 539.431 393.606 538.603 c
393.606 537.775 394.278 537.103 395.106 537.103 c
395.934 537.103 396.606 537.775 396.606 538.603 c
h
f*
396.606 538.603 m
396.606 539.431 395.934 540.103 395.106 540.103 c
394.278 540.103 393.606 539.431 393.606 538.603 c
393.606 537.775 394.278 537.103 395.106 537.103 c
395.934 537.103 396.606 537.775 396.606 538.603 c
h
S
Q
q
0.4 w
397.762 466.892 m
397.762 467.72 397.09 468.392 396.262 468.392 c
395.434 468.392 394.762 467.72 394.762 466.892 c
394.762 466.064 395.434 465.392 396.262 465.392 c
397.09 465.392 397.762 466.064 397.762 466.892 c
h
f*
397.762 466.892 m
397.762 467.72 397.09 468.392 396.262 468.392 c
395.434 468.392 394.762 467.72 394.762 466.892 c
394.762 466.064 395.434 465.392 396.262 465.392 c
397.09 465.392 397.762 466.064 397.762 466.892 c
h
S
Q
q
0.4 w
348.606 422.94 m
348.606 423.768 347.934 424.44 347.106 424.44 c
346.278 424.44 345.606 423.768 345.606 422.94 c
345.606 422.112 346.278 421.44 347.106 421.44 c
347.934 421.44 348.606 422.112 348.606 422.94 c
h
f*
348.606 422.94 m
348.606 423.768 347.934 424.44 347.106 424.44 c
346.278 424.44 345.606 423.768 345.606 422.94 c
345.606 422.112 346.278 421.44 347.106 421.44 c
347.934 421.44 348.606 422.112 348.606 422.94 c
h
S
Q
q
0.4 w
278.051 416.868 m
278.051 417.696 277.379 418.368 276.551 418.368 c
275.723 418.368 275.051 417.696 275.051 416.868 c
275.051 416.04 275.723 415.368 276.551 415.368 c
277.379 415.368 278.051 416.04 278.051 416.868 c
h
f*
278.051 416.868 m
278.051 417.696 277.379 418.368 276.551 418.368 c
275.723 418.368 275.051 417.696 275.051 416.868 c
275.051 416.04 275.723 415.368 276.551 415.368 c
277.379 415.368 278.051 416.04 278.051 416.868 c
h
S
Q
q
0.4 w
219.642 449.543 m
219.642 450.371 218.97 451.043 218.142 451.043 c
217.314 451.043 216.642 450.371 216.642 449.543 c
216.642 448.715 217.314 448.043 218.142 448.043 c
218.97 448.043 219.642 448.715 219.642 449.543 c
h
f*
219.642 449.543 m
219.642 450.371 218.97 451.043 218.142 451.043 c
217.314 451.043 216.642 450.371 216.642 449.543 c
216.642 448.715 217.314 448.043 218.142 448.043 c
218.97 448.043 219.642 448.715 219.642 449.543 c
h
S
Q
q
0.4 w
199.69 511.422 m
199.69 512.25 199.018 512.922 198.19 512.922 c
197.362 512.922 196.69 512.25 196.69 511.422 c
196.69 510.594 197.362 509.922 198.19 509.922 c
199.018 509.922 199.69 510.594 199.69 511.422 c
h
f*
199.69 511.422 m
199.69 512.25 199.018 512.922 198.19 512.922 c
197.362 512.922 196.69 512.25 196.69 511.422 c
196.69 510.594 197.362 509.922 198.19 509.922 c
199.018 509.922 199.69 510.594 199.69 511.422 c
h
S
Q
q
0.4 w
215.016 550.169 m
215.016 550.998 214.344 551.669 213.516 551.669 c
212.687 551.669 212.016 550.998 212.016 550.169 c
212.016 549.341 212.687 548.669 213.516 548.669 c
214.344 548.669 215.016 549.341 215.016 550.169 c
h
f*
215.016 550.169 m
215.016 550.998 214.344 551.669 213.516 551.669 c
212.687 551.669 212.016 550.998 212.016 550.169 c
212.016 549.341 212.687 548.669 213.516 548.669 c
214.344 548.669 215.016 549.341 215.016 550.169 c
h
S
Q
q
0.4 w
237.57 568.965 m
237.57 569.793 236.898 570.465 236.07 570.465 c
235.241 570.465 234.57 569.793 234.57 568.965 c
234.57 568.136 235.241 567.465 236.07 567.465 c
236.898 567.465 237.57 568.136 237.57 568.965 c
h
f*
237.57 568.965 m
237.57 569.793 236.898 570.465 236.07 570.465 c
235.241 570.465 234.57 569.793 234.57 568.965 c
234.57 568.136 235.241 567.465 236.07 567.465 c
236.898 567.465 237.57 568.136 237.57 568.965 c
h
S
Q
q
[1 0 0 1 268.05 588.181] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(a) 5.27043 Tj
5.266 -1.494 Td
/F7_0 6.974 Tf
(1) 3.96821 Tj
Q
q
[1 0 0 1 355.136 585.312] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(a) 5.27043 Tj
5.266 -1.494 Td
/F7_0 6.974 Tf
(2) 3.96821 Tj
Q
q
[1 0 0 1 401.178 541.205] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(a) 5.27043 Tj
5.266 -1.494 Td
/F7_0 6.974 Tf
(3) 3.96821 Tj
Q
q
[1 0 0 1 402.2 459.858] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(a) 5.27043 Tj
5.266 -1.494 Td
/F7_0 6.974 Tf
(4) 3.96821 Tj
Q
q
[1 0 0 1 348.262 410.218] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(a) 5.27043 Tj
5.266 -1.494 Td
/F7_0 6.974 Tf
(5) 3.96821 Tj
Q
q
[1 0 0 1 271.058 405.013] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(a) 5.27043 Tj
5.266 -1.494 Td
/F7_0 6.974 Tf
(6) 3.96821 Tj
Q
q
[1 0 0 1 206.112 439.731] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(a) 5.27043 Tj
5.266 -1.494 Td
/F7_0 6.974 Tf
(7) 3.96821 Tj
Q
q
[1 0 0 1 181.997 508.82] cm
[1 0 0 1 0 1.494] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(a) 5.27043 Tj
5.266 -1.494 Td
/F7_0 6.974 Tf
(8) 3.96821 Tj
Q
q
[1 0 0 1 173.322 547.857] cm
[1 0 0 1 0 2.85] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(a) 5.27043 Tj
5.266 -1.494 Td
/F7_0 6.974 Tf
(9) 3.96821 Tj
12.503 0 Td
/F10_0 9.963 Tf
(=) 7.75121 Tj
23.019 0 Td
/F4_0 9.963 Tf
(a) 5.27043 Tj
28.285 -1.494 Td
/F13_0 6.974 Tf
(\014) 4.51915 Tj
Q
q
[1 0 0 1 230.575 575.904] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
0 0 Td
/F4_0 9.963 Tf
(a) 5.27043 Tj
Q
q
1.2 w
271.954 580.717 m
299.674 565.521 l
323.311 541.068 l
314.345 492.978 l
284.187 449.778 l
254.843 447.332 l
218.142 449.543 l
198.19 511.422 l
213.515 550.169 l
236.069 568.964 l
271.954 580.717 l
h
S
Q
q
[4] 0 d
0.4 w
323.311 541.068 m
349.394 519.061 l
353.47 481.566 l
329.017 456.298 l
284.187 449.778 l
323.311 541.068 l
h
S
Q
q
[1 0 0 1 325.997 510.278] cm
0 g
0 G
[1 0 0 1 0 0] Tm
0 0 Td
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Q
q
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Q
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4.311 -1.494 Td
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(4) 3.96821 Tj
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4.311 -1.494 Td
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Q
q
[1 0 0 1 288.028 443.366] cm
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(c) 4.31398 Tj
4.311 -1.494 Td
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Q
q
[1 0 0 1 238.454 472.217] cm
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Q
q
[1 0 0 1 240.954 530.717] cm
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Q
q
0.4 w
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367.826 493.231 l
S
q
367.826 493.231 m
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367.826 493.231 l
h
f*
367.826 493.231 m
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375.046 494.755 l
367.826 493.231 l
h
S
Q
Q
q
[1 0 0 1 426.454 483.717] cm
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0 G
[1 0 0 1 0 0] Tm
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28 TJm
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Q
q
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Fm(b)1828 5484 y Fg(2)1865 5472 y Fm(c)1901 5484 y Fg(2)1938
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y Fg(7)2128 5472 y Fm(a)2172 5484 y Fg(7)2209 5472 y
Fm(a)2253 5484 y Fg(8)2304 5472 y Fm(:)14 b(:)g(:)f(a)2458
5484 y Fe(\014)2503 5472 y Fm(a)28 b Fn(\(for)f Fm(\014)g
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Fm(d)g Fn(do)r(es)g(not)g(lie)f(in)h(the)h(p)r(en)n(tagon)d
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b(:)g(:)g(:)g(;)g(c)3221 502 y Fe(\014)3265 490 y Fj(g)p
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b Fj(j)28 b Fn(=)f Fm(\014)t Fn(,)k(eac)n(h)f(triangle)f
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2610 y(in)i(the)h(case)e Fm(D)h Fj(6)p Fn(=)d Fj(;)i
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3577 y Fn(con)n(v)p Fm(X)7 b Fl(.)37 b(Then)28 b Fj(j)p
Fm(Y)18 b Fj(j)23 b(\024)g Fn(5)j Fl(and)i Fj(j)p Fm(X)7
b Fj(j)22 b(\024)h Fn(7)p Fl(.)37 b(\(Thus,)28 b(if)g
Fm(D)d Fn(=)d Fj(;)27 b Fl(in)g(the)f(pr)l(o)l(of)i(of)g(The)l(or)l(em)
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Fn(5)29 b Fl(and)i Fj(j)p Fm(B)t Fj(j)23 b(\024)g Fn(7)p
Fl(.\))330 3860 y(Pr)l(o)l(of.)86 b Fn(The)27 b(b)r(ound)g(on)g
Fj(j)p Fm(Y)19 b Fj(j)27 b Fn(is)g(ob)n(vious.)36 b(If)27
b Fm(Y)42 b Fn(=)23 b Fj(;)j Fn(then)i Fj(j)p Fm(X)7
b Fj(j)22 b(\024)h Fn(5)k(and)g(the)g(lemma)g(holds.)330
3959 y(If)34 b(1)f Fj(\024)g(j)p Fm(Y)19 b Fj(j)33 b(\024)g
Fn(2)h(then)g(w)n(e)f(de\014ne)h(an)g(auxiliary)e(line)i
Fm(l)h Fn(as)f(follo)n(ws.)54 b(If)34 b Fj(j)p Fm(Y)19
b Fj(j)33 b Fn(=)g(1)h(then)g Fm(l)h Fn(is)330 4059 y(c)n(hosen)26
b(as)g(a)h(line)g(connecting)f(the)i(p)r(oin)n(t)f(of)g
Fm(Y)46 b Fn(with)27 b(an)g(arbitrary)e(p)r(oin)n(t)i(of)g
Fm(X)7 b Fn(.)36 b(If)27 b Fj(j)p Fm(Y)19 b Fj(j)k Fn(=)f(2)330
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(p)r(oin)n(ts)h(of)f Fm(X)7 b Fn(.)37 b(It)28 b(follo)n(ws)e(that)i
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b Fn(in)19 b(the)f(clo)r(c)n(kwise)g(order)f(b)n(y)h
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y Fg(2)3045 4358 y Fm(;)g(:)g(:)g(:)f(;)h(y)3270 4373
y Fb(j)p Fe(Y)g Fb(j)3367 4358 y Fn(.)330 4457 y(F)-7
b(or)32 b Fj(j)p Fm(Y)19 b Fj(j)32 b Fn(=)g(3,)i(let)f
Fm(s)989 4469 y Fg(1)1027 4457 y Fm(;)14 b(s)1103 4469
y Fg(2)1140 4457 y Fm(;)g(s)1216 4469 y Fg(3)1253 4457
y Fm(;)g(t)1320 4469 y Fg(1)1357 4457 y Fm(;)g(t)1424
4469 y Fg(2)1461 4457 y Fm(;)g(t)1528 4469 y Fg(3)1598
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Fm(X)39 b Fn(lying)33 b(in)g(the)g(six)330 4557 y(regions)26
b(depicted)i(in)g(the)g(left)g(picture)g(in)g(Figure)f(8.)36
b(Then)1208 4740 y Fm(s)1247 4752 y Fe(i)1293 4740 y
Fn(+)18 b Fm(t)1406 4752 y Fe(i)1452 4740 y Fn(+)g Fm(s)1574
4752 y Fe(i)p Fg(+1)1769 4740 y Fj(\024)82 b Fn(3)55
b(\()p Fm(i)23 b Fn(=)g(1)p Fm(;)14 b Fn(2)p Fm(;)g Fn(3\))p
Fm(;)1628 4864 y(t)1658 4876 y Fe(i)1769 4864 y Fj(\024)82
b Fn(2)55 b(\()p Fm(i)23 b Fn(=)g(1)p Fm(;)14 b Fn(2)p
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y Fg(3)415 5346 y Fn(\))g(+)f(\()p Fm(u)629 5358 y Fg(4)684
5346 y Fn(+)g Fm(u)815 5358 y Fg(5)852 5346 y Fn(\))h(+)f(\()p
Fm(u)1066 5358 y Fg(6)1121 5346 y Fn(+)g Fm(u)1252 5358
y Fg(7)1307 5346 y Fn(+)g Fm(u)1438 5358 y Fg(8)1475
5346 y Fn(\))23 b Fj(\024)g Fn(3)18 b(+)g(1)g(+)g(3)23
b(=)f(7)27 b(in)h(this)g(case.)455 5445 y(If)20 b Fj(j)p
Fm(Y)f Fj(j)k Fn(=)f(5)e(then)g(the)h(\014v)n(e)e(shaded)h(4-sectors)e
Fm(S)5 b Fn(\()p Fm(y)2010 5457 y Fe(i)p Fb(\000)p Fg(1)2122
5445 y Fm(;)14 b(y)2200 5457 y Fe(i)2227 5445 y Fm(;)g(y)2305
5457 y Fe(i)p Fg(+1)2417 5445 y Fm(;)g(y)2495 5457 y
Fe(i)p Fg(+2)2606 5445 y Fn(\))20 b(in)g(the)h(righ)n(t)e(picture)330
5545 y(in)26 b(Figure)f(8)g(con)n(tain)g(no)h(p)r(oin)n(t)g(of)f
Fm(X)32 b Fn(\(b)n(y)26 b(Observ)-5 b(ation)24 b(2\).)36
b(Therefore)25 b(eac)n(h)g(p)r(oin)n(t)h(of)f Fm(X)32
b Fn(is)330 5645 y(separated)18 b(from)h(con)n(v)p Fm(Y)38
b Fn(b)n(y)19 b(at)h(least)e(t)n(w)n(o)h(of)g(the)h(\014v)n(e)f(lines)g
Fm(y)2259 5657 y Fe(i)2287 5645 y Fm(y)2328 5657 y Fe(i)p
Fg(+1)2439 5645 y Fn(.)34 b(If)20 b Fj(j)p Fm(X)7 b Fj(j)23
b Fm(>)f Fn(7)d(w)n(as)f(satis\014ed,)1809 5919 y(7)p
eop end
%%Page: 8 8
TeXDict begin 8 7 bop 330 1115 a @beginspecial 83 @llx
527 @lly 478 @urx 623 @ury 3950 @rwi @setspecial
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%!PS-Adobe-3.0 EPSF-3.0
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%%LanguageLevel: 2
%%BoundingBox: 83 527 478 623
%%HiResBoundingBox: 83.4113 527.79 477.551 622.927
%%DocumentSuppliedResources: (atend)
%%EndComments
%%BeginProlog
%%BeginResource: procset xpdf 2.01 0
/xpdf 75 dict def xpdf begin
% PDF special state
/pdfDictSize 14 def
/pdfSetup {
3 1 roll 2 array astore
/setpagedevice where {
pop 3 dict begin
/PageSize exch def
/ImagingBBox null def
/Policies 1 dict dup begin /PageSize 3 def end def
{ /Duplex true def } if
currentdict end setpagedevice
} {
pop pop
} ifelse
} def
/pdfStartPage {
pdfDictSize dict begin
/pdfFill [0] def
/pdfStroke [0] def
/pdfLastFill false def
/pdfLastStroke false def
/pdfTextMat [1 0 0 1 0 0] def
/pdfFontSize 0 def
/pdfCharSpacing 0 def
/pdfTextRender 0 def
/pdfTextRise 0 def
/pdfWordSpacing 0 def
/pdfHorizScaling 1 def
} def
/pdfEndPage { end } def
% separation convention operators
/findcmykcustomcolor where {
pop
}{
/findcmykcustomcolor { 5 array astore } def
} ifelse
/setcustomcolor where {
pop
}{
/setcustomcolor {
exch
[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
0 4 getinterval cvx
[ exch /dup load exch { mul exch dup } /forall load
/pop load dup ] cvx
] setcolorspace setcolor
} def
} ifelse
/customcolorimage where {
pop
}{
/customcolorimage {
gsave
[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
0 4 getinterval cvx
[ exch /dup load exch { mul exch dup } /forall load
/pop load dup ] cvx
] setcolorspace
10 dict begin
/ImageType 1 def
/DataSource exch def
/ImageMatrix exch def
/BitsPerComponent exch def
/Height exch def
/Width exch def
/Decode [1 0] def
currentdict end
image
grestore
} def
} ifelse
% PDF color state
/sCol {
pdfLastStroke not {
pdfStroke aload length
dup 1 eq {
pop setgray
}{
dup 3 eq {
pop setrgbcolor
}{
4 eq {
setcmykcolor
}{
findcmykcustomcolor exch setcustomcolor
} ifelse
} ifelse
} ifelse
/pdfLastStroke true def /pdfLastFill false def
} if
} def
/fCol {
pdfLastFill not {
pdfFill aload length
dup 1 eq {
pop setgray
}{
dup 3 eq {
pop setrgbcolor
}{
4 eq {
setcmykcolor
}{
findcmykcustomcolor exch setcustomcolor
} ifelse
} ifelse
} ifelse
/pdfLastFill true def /pdfLastStroke false def
} if
} def
% build a font
/pdfMakeFont {
4 3 roll findfont
4 2 roll matrix scale makefont
dup length dict begin
{ 1 index /FID ne { def } { pop pop } ifelse } forall
/Encoding exch def
currentdict
end
definefont pop
} def
/pdfMakeFont16 {
exch findfont
dup length dict begin
{ 1 index /FID ne { def } { pop pop } ifelse } forall
/WMode exch def
currentdict
end
definefont pop
} def
/pdfMakeFont16L3 {
1 index /CIDFont resourcestatus {
pop pop 1 index /CIDFont findresource /CIDFontType known
} {
false
} ifelse
{
0 eq { /Identity-H } { /Identity-V } ifelse
exch 1 array astore composefont pop
} {
pdfMakeFont16
} ifelse
} def
% graphics state operators
/q { gsave pdfDictSize dict begin } def
/Q { end grestore } def
/cm { concat } def
/d { setdash } def
/i { setflat } def
/j { setlinejoin } def
/J { setlinecap } def
/M { setmiterlimit } def
/w { setlinewidth } def
% color operators
/g { dup 1 array astore /pdfFill exch def setgray
/pdfLastFill true def /pdfLastStroke false def } def
/G { dup 1 array astore /pdfStroke exch def setgray
/pdfLastStroke true def /pdfLastFill false def } def
/rg { 3 copy 3 array astore /pdfFill exch def setrgbcolor
/pdfLastFill true def /pdfLastStroke false def } def
/RG { 3 copy 3 array astore /pdfStroke exch def setrgbcolor
/pdfLastStroke true def /pdfLastFill false def } def
/k { 4 copy 4 array astore /pdfFill exch def setcmykcolor
/pdfLastFill true def /pdfLastStroke false def } def
/K { 4 copy 4 array astore /pdfStroke exch def setcmykcolor
/pdfLastStroke true def /pdfLastFill false def } def
/ck { 6 copy 6 array astore /pdfFill exch def
findcmykcustomcolor exch setcustomcolor
/pdfLastFill true def /pdfLastStroke false def } def
/CK { 6 copy 6 array astore /pdfStroke exch def
findcmykcustomcolor exch setcustomcolor
/pdfLastStroke true def /pdfLastFill false def } def
% path segment operators
/m { moveto } def
/l { lineto } def
/c { curveto } def
/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
neg 0 rlineto closepath } def
/h { closepath } def
% path painting operators
/S { sCol stroke } def
/Sf { fCol stroke } def
/f { fCol fill } def
/f* { fCol eofill } def
% clipping operators
/W { clip newpath } def
/W* { eoclip newpath } def
% text state operators
/Tc { /pdfCharSpacing exch def } def
/Tf { dup /pdfFontSize exch def
dup pdfHorizScaling mul exch matrix scale
pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put
exch findfont exch makefont setfont } def
/Tr { /pdfTextRender exch def } def
/Ts { /pdfTextRise exch def } def
/Tw { /pdfWordSpacing exch def } def
/Tz { /pdfHorizScaling exch def } def
% text positioning operators
/Td { pdfTextMat transform moveto } def
/Tm { /pdfTextMat exch def } def
% text string operators
/awcp { % awidthcharpath
exch {
1 string dup 0 3 index put 2 index charpath
3 index 3 index rmoveto
4 index eq { 5 index 5 index rmoveto } if
} forall
6 {pop} repeat
} def
/Tj { fCol
0 pdfTextRise pdfTextMat dtransform rmoveto
1 index stringwidth pdfTextMat idtransform pop
sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse
pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32
4 3 roll pdfCharSpacing pdfHorizScaling mul add 0
pdfTextMat dtransform
6 5 roll
currentpoint 8 2 roll
pdfTextRender 1 and 0 eq {
6 copy awidthshow
} if
pdfTextRender 3 and dup 1 eq exch 2 eq or {
8 6 roll moveto
currentfont /FontType get 3 eq { fCol } { sCol } ifelse
false awcp currentpoint stroke moveto
} {
8 {pop} repeat
} ifelse
0 pdfTextRise neg pdfTextMat dtransform rmoveto } def
/Tj16 { pdfTextRender 1 and 0 eq { fCol } { sCol } ifelse
0 pdfTextRise pdfTextMat dtransform rmoveto
2 index stringwidth pdfTextMat idtransform pop
sub exch div
pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32
4 3 roll pdfCharSpacing pdfHorizScaling mul add 0
pdfTextMat dtransform
6 5 roll awidthshow
0 pdfTextRise neg pdfTextMat dtransform rmoveto } def
/Tj16V { pdfTextRender 1 and 0 eq { fCol } { sCol } ifelse
0 pdfTextRise pdfTextMat dtransform rmoveto
2 index stringwidth pdfTextMat idtransform exch pop
sub exch div
0 pdfWordSpacing pdfTextMat dtransform 32
4 3 roll pdfCharSpacing add 0 exch
pdfTextMat dtransform
6 5 roll awidthshow
0 pdfTextRise neg pdfTextMat dtransform rmoveto } def
/TJm { pdfFontSize 0.001 mul mul neg 0
pdfTextMat dtransform rmoveto } def
/TJmV { pdfFontSize 0.001 mul mul neg 0 exch
pdfTextMat dtransform rmoveto } def
% Level 1 image operators
/pdfIm1 {
/pdfImBuf1 4 index string def
{ currentfile pdfImBuf1 readhexstring pop } image
} def
/pdfIm1Sep {
/pdfImBuf1 4 index string def
/pdfImBuf2 4 index string def
/pdfImBuf3 4 index string def
/pdfImBuf4 4 index string def
{ currentfile pdfImBuf1 readhexstring pop }
{ currentfile pdfImBuf2 readhexstring pop }
{ currentfile pdfImBuf3 readhexstring pop }
{ currentfile pdfImBuf4 readhexstring pop }
true 4 colorimage
} def
/pdfImM1 {
/pdfImBuf1 4 index 7 add 8 idiv string def
{ currentfile pdfImBuf1 readhexstring pop } imagemask
} def
% Level 2 image operators
/pdfImBuf 100 string def
/pdfIm {
image
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
/pdfImSep {
findcmykcustomcolor exch
dup /Width get /pdfImBuf1 exch string def
begin Width Height BitsPerComponent ImageMatrix DataSource end
/pdfImData exch def
{ pdfImData pdfImBuf1 readstring pop
0 1 2 index length 1 sub {
1 index exch 2 copy get 255 exch sub put
} for }
6 5 roll customcolorimage
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
/pdfImM {
fCol imagemask
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
end
%%EndResource
%%EndProlog
%%BeginSetup
xpdf begin
%%BeginResource: font BAPEMX+CMMI9
%!PS-AdobeFont-1.1: CMMI9 1.100
%%CreationDate: 1996 Jul 23 07:53:55
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /BAPEMX+CMMI9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 121 /y put
readonly def
/FontBBox{-29 -250 1075 750}readonly def
/UniqueID 5087384 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font UCXSEZ+CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /UCXSEZ+CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F7_0 /UCXSEZ+CMR6 1 1
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pdfMakeFont
%%BeginResource: font EGOODC+CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /EGOODC+CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 99 /c put
dup 110 /n put
dup 111 /o put
dup 118 /v put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F10_0 /EGOODC+CMR10 1 1
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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef]
pdfMakeFont
%%BeginResource: font THXGDS+CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /THXGDS+CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 89 /Y put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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