Unpublished texts 

  1. Solving the diophantine equation x2-y3=+- 1, Matematické Obzory 32 (1989), 47-53, in Czech.  abstract 
  2. On a proof of Ramsey theorem and of Erdös-Rado theorem for pairs, KAM Series preprint no. 256 (1993), 5 p. abstract   
  3. Note on the maximum size of a Sidon set, KAM Series preprint no. 356 (1997), 5 p.  abstract 
  4. Bárány and Larman's combinatorial approach to the circle problem , KAM-DIMATIA Series preprint no. 420 (1999), 15 p.  abstract 
  5. Extremal problems (and a bit of enumeration) for hypergraphs with linearly ordered vertex sets , ITI Series preprint no. 021 (2001), 40 p.  abstract (most of this material was eventually published in my papers 27 and 28)
  6. Irreducible and connected permutations , ITI Series preprint no. 122 (2003), 24 p.  abstract 
  7. Enumerative and extremal combinatorics of a containment relation of partitions and hypergraphs, 2003, 51+123 p. (habilitation thesis, written 2001, defended 2003).
  8. What are Davenport-Schinzel sequences and what are they for, in preparation, 2004. (As of 2013, it remains forever in preparation.)
  9. Non-holonomicity of the sequence log 1, log 2, log 3, ..., arXiv:math.CO/0502141.
  10. Note on the number of proper colorings of a graph, arXiv:math.CO/0609179.
  11. A detailed derivation of the transfer matrix method formula, June 2008.
  12. A question on linear independence of square roots, August 2009.
  13. Real numbers as infinite decimals and irrationality of 2^{1/2}, arXiv:0910.5870 , October 2009.
  14. On Furstenberg's topological proof of the infinitude of primes, February 2010.
  15. Stormer's solution of the unit equation x - y = 1, August 2010.
  16. On the theorem of Duminil-Copin and Smirnov about the number of self-avoiding walks in the hexagonal lattice, arXiv:1102.5733 , March 2011.
  17. A generating functions proof of this partition identity: the sum over all partitions of a number n with mutually distinct parts, each partition weighted by (-1)^{k+1}.m where k is the number of parts and m the smallest part, equals to the number of divisors of n, May 2012.
  18. Polymath's combinatorial proof of the density Hales-Jewett theorem, arXiv:1205.7084 , May 2012. Comment (December 2012). Much shorter (cca 10 pages) combinatorial proof of the density Hales-Jewett theorem, than Polymath's, was given by P. Dodos, V. Kanellopoulos and K. Tyros in arXiv:1209.4986 in September 2012. This seems to me at present to be the simplest (self-contained) proof of the DHJ theorem and, a fortiori, of Szemerédi's theorem.
  19. Shifted squares n^2+1 have in average (3/pi)log n divisors , August 2012.
  20. Szemerédi's proof of Roth's theorem that r_3(n) = o(n) , April 2013.

last updated: April 2013