Plan of the course <b>Combinatorial Counting</b> in summer term 2025/26
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The symbolic method, Catalan numbers and Polya's theorem
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Numbers of SAWs in the hexagonal grid
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Some results from the book A. Barvinok - Combinatorics and Complexity of
Partition Functions
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<a href="COMCOU_LN26.pdf">lecture notes</a> (preliminary, updated April 17, 2026)
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Lecture 1, February 20, 2026
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A derivation of the formula for the Catalan numbers C_n
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Lecture 2, February 27, 2026
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What is (1 - 4x)^{1/2}?
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Lecture 3, March 6, 2026
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Four proofs that (C_n) is not a linear recurrence sequence
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Lecture 4, March 13, 2026
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Polya's theorem on random walks in the grid graph Z^d via the symbolic 
method
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Lecture 5, March 20, 2026
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Counting paths in the hexagonal graph 1. Existence of the growth constant 
for LFT (locally finite transitive) graphs
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Lecture 6, March 27, 2026
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Counting paths in the hexagonal graph 2. The general identity
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April 3, 2026
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no lecture - Good Friday
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Lecture 7, April 10, 2026
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Counting paths in the hexagonal graph 3. The lower bound kappa >= 2cos(pi/8)
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Lecture 8, April 17, 2026
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Counting paths in the hexagonal graph 4. Series of fps and the grouping theorem. 
The upper bound kappa <= 2cos(pi/8)
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