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User:Vaclav Kotesovec

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Born in 1956, living in Prague, Czech republic. I am now retired.
International master of the FIDE for chess compositions.
Interests: chess problems, combinatorics, asymptotics, partitions, generating functions and series, functions of complex variables.

Mathematical articles and books by Vaclav Kotesovec:

  • Non-attacking chess pieces (PDF, 14 MB) - sixth edition, 795 pages, over 500 formulas, many tables, published Feb 02 2013 (minor update Mar 29 2016). A book is devoted to the question of the number of arrangements of non-attacking chess pieces of the same kind on chessboards of various sizes and types. The best-known example is the n-Queens problem, but this publication has a much wider range and includes other chess pieces (kings, rooks, bishops, knights) and many fairy pieces. Even though the book is about chess and each problem can be placed among chess-mathematical problems, it will be more readily understandable by mathematicians than by chess players or composers. A partial knowledge of linear algebra, difference equations, generating functions and power series is necessary.

  • A method of finding the asymptotics of q-series based on the convolution of generating functions - arXiv:1509.08708 [math.CO], Sep 29 2015 (minor update Mar 07 2016)
  • Asymptotics of the Euler transform of Fibonacci numbers - arXiv:1508.01796 [math.CO], Aug 07 2015
  • The partition factorial constant and asymptotics of the sequence A058694, mirror - Jun 26 2015
  • The integration of q-series, mirror - May 29 2015, updated May 31 2015
  • Asymptotics of the sequence A120733, mirror - May 03 2015
  • Asymptotics of sequence A034691, mirror - application of the saddle-point method (Sep 09 2014)
  • Asymptotic of the coefficients A079330 / A088989, mirror - about roots of the equation tan(x)=x (Aug 20 2014)
  • Asymptotic solution of the equations using the Lambert W-function, mirror - method of solution of the equations, with an application of the theorem by Hayman (Aug 08 2014)
  • Asymptotic of subsequences of A212382, mirror - application of the theorem by Bender for ordinary generating functions (Jul 17 2014)
  • Asymptotic of sequences A161630, A212722, A212917 and A245265, mirror - application of the theorem by Bender for exponential generating functions (Jul 16 2014)
  • Asymptotic of sequences A244820, A244821 and A244822, mirror (Jul 11 2014)
  • Asymptotic of implicit functions if Fww = 0 - extension of theorem by Bender (Jan 19 2014)
  • Asymptotic of sequence A227403 - rigorous proof and conjecture (Sep 21 2013)
  • Asymptotic of Young tableaux of bounded height - conjecture (Sep 12 2013)
  • Asymptotic of sequence A084611 (Jul 26 2013)
  • Interesting asymptotic formulas for binomial sums (Jun 09 2013, extended Jun 28 2013)
  • Asymptotic of generalized ApĂ©ry sequences with powers of binomial coefficients (Nov 04 2012, extended Nov 23 2012)
  • Too many errors around coefficient C1 in asymptotic of sequence A002720 - I found bug in program Mathematica! (Sep 28 2012). Update Jul 25 2015: This bug was fixed in version 10.2.0.0 / July 2015.
  • Asymptotic of a sums of powers of binomial coefficients * x^k (Sep 20 2012)
  • Asymptotic formula for number of fat trees on n labeled vertices - OEIS A055779 (Aug 27 2012)


    Electronic edition of chess books by Vaclav Kotesovec:
  • vol.1 30 years of cyclical pin (1977-2007) - PDF (0,5 MB), 24 pages, 35 problems, Nov 08 2007
  • vol.2 Fairy chess endgames - new results 2008 - PDF (0,7 MB), 46 pages, 61 diagrams, May 14 2008
  • vol.3 234 best chess problems - PDF (5 MB), 320 pages, 609 diagrams, many photos and tables, Sep 03 2008, printed book Sep 22 2008
  • vol.4 Application of Graph Theory in Chess Problems - Dual-free Leaper and Hopper tours, PDF (3 MB), 76 pages, 280 diagrams, 33 graphs, 20 tables, May 31 2009, Grasshopper Tours - English summary about "Hopper Tours" by John Beasley (Variant Chess 61, July 2009, p.115).
  • vol.5 Records in maximummers and minimummers - PDF (3 MB), 304 pages, 612 problems, 1225 diagrams, 35 tables, Jul 24 2009
  • vol.6 Non-attacking chess pieces - PDF (14 MB), 795 pages, over 500 formulas, many tables and graphs. First edition Apr 22 2010, second edition Jun 23 2010, third edition Jan 19 2011, fourth edition Jun 15 2011, fifth edition Jan 09 2012, sixth edition Feb 02 2013
  • vol.7 Fairy twomovers 2008-2010 - PDF (2 MB), 54 pages, 36 twomovers, 54 diagrams, Feb 28 2011
  • vol.8 Fairy chess endings on an n x n chessboard - PDF (20 MB), 410 pages, 1186 diagrams, 20 tables and 30 graphs, Jul 19 2013
  • vol.9 Records in five-man fairy helpmates - PDF (0,5 MB), 61 pages, 196 helpmates, 392 diagrams, 14 tables, Oct 14 2013

    Other my chess books and articles:
  • 500 triple echoes in helpplay - PDF (14,3 MB), 1998, booklet, 108 pages
  • Echoes in long helpmates - PDF (1,4 MB), 2002, book, 140 pages, 1561 diagrams
  • King and Two Generalised Knights against King, ICGA Journal, Vol. 24, No. 2, pp. 105-107 (2001)

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