Unpublished texts 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.

  21. Why is the number 0.23571113171923... irrational? , July 2013 (in preparation).

  22. Schur's asymptotics for p_A(n) , January 2014 (for the course Introduction to Number Theory).

  23. Every binary word is, almost, a shuffle of twin subsequences - a theorem of Axenovich, Person and Puzynina, August 2015.

  24. There is no free will: almost every value of every function is predetermined by earlier values, August 2015.
  25. The Fundamental Theorem of Algebra, October 2015.
  26. Path connectedness implies arc connectedness, November 2015 (in preparation).

  27. The Basel problem (1 + 1/4 + 1/9 + ... = pi^2/6) and the Riemann-Lebesgue lemma, December 2015.
  28. Entire function is globally analytic, January 2016. I plan to write an extended version including another proof, topological one that avoids integration completely (Whyburn, Porcelli--Connell, ...).  

  29. The Jordan curve (circuit) theorem, March 2016 (in preparation).

  30. Computing the n-th coefficient of an algebraic power series modulo p in O(log n) operations, May 2016. Also in arXiv.

  31. Moreira's theorem: any finite coloring of {1, 2, ...} has a monochromatic triple {x, x+y, xy}, after arXiv, May 2016.
  32. Roth's theorem for 3-term-AP-free subsets of Z_q^n, June 2016 (in preparation).
  33. Birch's theorem: if f(n) is multiplicative and has a non-decreasing normal order then f(n)=n^c, June 2016. Also in arXiv.
  34. Alimov's theorem: any ordered semigroup without infinitesimals is commutative, August 2016.
  35. Why does Euler's formula hold for the graph with one edge, May 2017.

last updated in May 2017