Born in 1956, living in Prague, Czech republic.
International Grandmaster of the FIDE for Chess Compositions.
Interests: chess problems, combinatorics, asymptotics, partitions, generating functions and series, functions of complex variables.
I'm retired now and I do math mostly for fun. I enjoy discovering new formulas, but article writing is a tedious job and takes a lot of time. That's why I publish many formulas and much less articles.
Mathematical articles and books by Vaclav Kotesovec:
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)
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.
Calculation of the asymptotic formula for the sequence A005366 - general formula published Apr 01 2021, Mathematica notebook added Sep 15 2024
Asymptotics for a certain group of exponential generating functions - arXiv:2207.10568 [math.CO], Jul 13 2022
Asymptotic formula for OEIS A032302 - published Jan 04 2016, Mathematica notebook added Jun 21 2022
L-convex polyominoes and 201-avoiding ascent sequences - with Anthony Guttmann, arXiv:2109.09928 [math.CO], Sep 21 2021
Asymptotics of sequence A002513, mirror - Aug 24 2019
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 Apéry 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)
Citations of my formulas from the OEIS in other articles:
Mathematical Constants II - Steven R. Finch, 2019, ISBN: 9781108470599, p. 76 [OEIS A000294 and A255939], p. 267 [OEIS A000670, A032032, A102233, and A232475], p. 269 and 271 [OEIS A034691], p. 496 [OEIS A062980 and A094199]
Enumerative Combinatorics - Richard P. Stanley (vol. 1, 2ed, 2012, p.640 and 615, exercise 41).
The number of {1243, 2134}-avoiding permutations - David Callan, arXiv:1303.3857 [math.CO], 15 Mar 2013, OEIS A164651
Injections, Surjections and More - Steven Finch, 07 May 2015
Integer Partitions - Steven Finch, updated in 2015, p.5
Errata and Addenda to Mathematical Constants - Steven Finch, updated Jan 22 2016, p.42 and 117, OEIS A003242 and A032032
Errata and Addenda to Mathematical Constants - Steven Finch, arXiv:2001.00578 [math.HO], Nov 03 2022, [632] p. 44 and 127 OEIS A003242, [691] p. 52, [692] p. 52 and 132 OEIS A002465
Mellin Transforms of the Generalized Fractional Integrals and Derivatives - Udita N. Katugampola, arXiv:1112.6031 [math.CA], 29 Oct 2014, OEIS A223168
Strong and ratio asymptotics for Laguerre polynomials revisited - Alfredo Deano, Edmundo J. Huertas, Francisco Marcellan, arXiv:1301.4266v2 [math.CA], 24 Jun 2013 (see Comments)
Two Vignettes On Full Rook Placements - J. Bloom, V. Vatter, arXiv:1310.6073 [math.CO], 22 Oct 2013, OEIS A165543
Two Vignettes On Full Rook Placements - J. Bloom, V. Vatter, The Australasian Journal of Combinatorics, vol. 64(1), 2016, p. 80, OEIS A165543
On a Mean Field Theory of Topological 2D Gravity - Jian Zhou, arXiv:1503.08546 [math.AG], 30 Mar 2015, OEIS A094199
Enumeration of standard Young tableaux of shifted strips with constant width - Ping Sun, arXiv:1506.07256 [math.CO], 24 Jun 2015, OEIS A181197
Polynomials, Quantum Query Complexity, and Grothendieck's Inequality - Scott Aaronson, Andris Ambainis, Janis Iraids, Martins Kokainis, Juris Smotrovs, arXiv:1511.08682 [quant-ph], 27 Nov 2015
Computationally Efficient Bounds for the Sum of Catalan Numbers - Kevin Topley, arXiv:1601.04223 [math.CO], 16 Jan 2016, OEIS A014138
Short note on the number of 1-ascents in dispersed dyck paths - Kairi Kangro, Mozhgan Pourmoradnasseri, Dirk Oliver Theis, arXiv:1603.01422 [math.CO], 04 Mar 2016, OEIS A191386
Efficient Counting of Degree Sequences or DOI - Kai Wang, arXiv:1604.04148 [math.CO], 14 Apr 2016, p. 2 and p. 13, OEIS A005155
Convergence criteria for FIW-algebras and polynomial statistics on maximal tori in type B/C - Rita Jimenez Rolland, Jennifer C. H. Wilson, arXiv:1604.06392 [math.CO], 21 Apr 2016, p. 14, OEIS A075196
Asymptotic enumeration by Khintchine-Meinardus method: Necessary and sufficient conditions for exponential growth - Boris Granovsky, arXiv:1606.08016 [math.CO], 26 Jun 2016, p. 2 and p. 29
Chained permutations and alternating sign matrices - inspired by three-person chess - Dylan Heuer, Chelsey Morrow, Ben Noteboom, Sara Solhjem, Jessica Striker, Corey Vorland, arXiv:1611.03387 [math.CO], 10 Nov 2016, p. 26 and p. 1
On the number of lattice convex chains - Julien Bureaux, Nathanaël Enriquez, arXiv:1603.09587 [math.PR], 31 Mar 2016 (updated 11 Dec 2016), p. 11 and p. 14, OEIS A267862
Some useful theorems for asymptotic formulas and their applications to skew plane partitions and cylindric partitions - Guo-Niu Han, Huan Xiong, arXiv:1707.04907 [math.CO], 16 Jul 2017, p. 1, 2 and 15. another version
Skew doubled shifted plane partitions: calculus and asymptotics - Guo-Niu Han, Huan Xiong, arXiv:1707.05832 [math.CO], 18 Jul 2017, p. 3, 10 and 17
k -Foldability of Words - B. Bjorkman, G. Cochran, W. Gao, L. Keough, R. Kirsch, M. Phillipson, D. Rorabaugh, H. Smith, J. Wise, arXiv:1710.10616 [math.CO], 29 Oct 2017, p. 13 (Acknowledgements)
A survey of known results and research areas for n-queens - Jordan Bell, Brett Stevens, Discrete Mathematics 309 (2009) 1–31, p. 20
Elementary Number Theory - Hatice Boylan and Nils-Peter Skoruppa, Lecture Notes Istanbul Universitesi and Universitat Siegen, 7/2016, p.85
On Certain Reciprocal Sums - Soumyadip Sahu, arXiv:1807.05454 [math.NT], 14 Jul 2018, p. 11, OEIS A248230, A248234
What is an answer? — remarks, results and problems on PIO formulas in combinatorial enumeration, part I - Martin Klazar, arXiv:1808.08449, Sep 11 2018, p.19, 38, 40, 46, 47, OEIS A000009, A000700, A292520, A002107, A258232.
A class of symmetric difference-closed sets related to commuting involutions - John M. Campbell, Discrete Mathematics and Theoretical Computer Science DMTCS vol. 19:1, 2017, #8, p.4, 7. OEIS A266503, A267840.
Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube - Yu Hin (Gary) Au, Fatemeh Bagherzadeh, Murray R. Bremner, arXiv:1903.00813, Mar 03 2019, p.10, 27. OEIS A236339. See also Journal of Integer Sequences, Vol. 23 (2020), Article 20.1.4.
On the asymptotic distinct prime partitions of integers - M. V. N. Murthy, M. Brack, R. K. Bhaduri, arXiv:1904.02776, Mar 22 2019, p. 10. OEIS A000586. New version May 10 2021, see p.10-11.
Exact finite-size corrections in the dimer model on a planar square lattice - Nikolay Sh. Izmailian, Vladimir V. Papoyan and Robert M. Ziff, Journal of Physics A: Mathematical and Theoretical, Jul 23 2019, p. 24, reference [48]. OEIS A012495.
Asymptotics and statistics on Fishburn matrices and their generalizations - Hsien-Kuei Hwang and Emma Yu Jin, arXiv:1911.06690 [math.CO], Nov 15 2019, p.33 OEIS A186737, p.35 OEIS A035378, p.36 OEIS A207557.
New results and conjectures on 2-partitions of multisets or DOI - Ovidiu Bagdasar and Dorin Andrica, 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO), 2017. OEIS A047653.
The r-alternating permutations, István Mező & José L. Ramírez, Aequationes mathematicae volume 94, pages 37–57 (2020). OEIS A225688.
Some inequalities for Garvan's bicrank function of 2-colored partitions - Shane Chern, Dazhao Tang, Liuquan Wang, arXiv:1805.06575 [math.CO], May 17 2018, p.3, p.27.
Phase transitions from exp(n^(1/2)) to exp(n^(2/3)) in the asymptotics of banded plane partitions - Wenjie Fang, Hsien-Kuei Hwang, Mihyun Kang, arXiv:2004.08901 [math.CO], Apr 19 2020, p.6 OEIS A266648, p.28 OEIS A225196-9.
Structure and enumeration of K4-minor-free links and link-diagrams - Juanjo Rué, Dimitrios M. Thilikos and Vasiliki Velona, arXiv:1806.07855 [math.CO], Apr 24 2020, p.17 (OEIS A022567) and p.29.
An introduction to the Bernoulli function - Peter H. N. Luschny, arXiv:2009.06743 [math.HO], Sep 11 2020, p.11 and p.33. HTML variant
Growth rate of 3D heaps of pieces - M.V. Tamm, N. Pospelov, S. Nechaev, arXiv:2009.12540 [cond-mat.stat-mech], Oct 02 2020, p.7-8 and 14.
On the largest Kronecker and Littlewood-Richardson coefficients - Igor Pak, Greta Panova, Damir Yeliussizov, arXiv:1804.04693 [math.CO], 2018, Remark 3.8, formula (3.5), p.8 - cited my asymptotic formula from OEIS A110143.
Asymptotics of descent functions - Kaarel Hänni, arXiv:2011.14360 [math.CO], Nov 29 2020, p. 14, OEIS A049774, A117158, A177523.
All-orders asymptotics of tensor model observables from symmetries of restricted partitions - Joseph Ben Geloun, Sanjaye Ramgoolam, arXiv:2106.01470 [hep-th], Jun 02 2021, p. 3, 5, 8, 19, 43. OEIS A110143, A279819.
Properties of Hamiltonian Circuits in Rectangular Grids - Rüdiger Jehn, arXiv:2103.15778 [math.GM], Mar 29 2021, p. 13, 16, OEIS A201629.
The Generalized Superfactorial, Hyperfactorial and Primorial functions - Vignesh Raman, arXiv:2012.00882 [math.NT], Dec 01 2020, p. 2, 17, OEIS A002109.
Bounds for Combinatorial Types of Non-Attacking Riders - Grant Jensen, arXiv:2006.12689 [math.CO], Jun 24 2020, p. 4, 5, 6.
Wilf Equivalences and Stanley-Wilf Limits for Patterns in Rooted Labeled Forests - Michael Ren, arXiv:2007.12690 [math.CO], Jul 27 2020, p. 48, OEIS A000262.
Dyson's Crank and the Mex of Integer Partitions - Brian Hopkins, James A. Sellers, Dennis Stanton, arXiv:2009.10873 [math.CO], Sep 23 2020, p. 4, OEIS A064410.
Bell number - Wikipedia, May 18 2021, OEIS A000110.
Quiddities of polygon dissections and the Conway-Coxeter frieze equation - Charles H. Conley and Valentin Ovsienko, arXiv:2107.01234 [math.CO], Jul 02 2021, p. 5, 6, 7, OEIS A218251.
Transportation Distance between Probability Measures on the Infinite Regular Tree - Pakawut Jiradilok and Supanat Kamtue, arXiv:2107.09876 [math.CO], Sep 18 2021, p.36, 37, OEIS A035610, A130976.
Closed-form formulas and properties of coefficients in Maclaurin's series expansion of Wilf's function - Feng Qi and Mark Daniel Ward, arXiv:2110.08576 [math.CO], Oct 16 2021, p. 20, 24, OEIS A014307, A180875.
Pattern-avoiding ascent sequences of length 3 - Andrew R. Conway, Miles Conway, Andrew Elvey Price and Anthony J. Guttmann, arXiv:2111.01279 [math.CO], Nov 01 2021, p. 3, 31, OEIS A202062.
Guessing with Little Data - Manuel Kauers and Christoph Koutschan, arXiv:2202.07966 [cs.SC], Feb 16 2022, p. 15, 17, OEIS A189281.
Counting Permutations Where The Difference Between Entries Located r Places Apart Can never be s (For any given positive integers r and s) - George Spahn and Doron Zeilberger, arXiv:2211.02550 [math.CO], Dec 06 2022, p. 2, 7, OEIS A189281, A189282, A189283, A189284, A189285 and A110128.
Maximum arrangements of nonattacking kings on the 2n×2n chessboard - Tricia Muldoon Brown, arXiv:2111.10331 [math.CO], Nov 19 2021, p. 2, 8, OEIS A018807.
Combinatorial Exploration: An algorithmic framework for enumeration - Michael H. Albert, Christian Bean, Anders Claesson, Émile Nadeau, Jay Pantone, Henning Ulfarsson, arXiv:2202.07715 [math.CO], Feb 15 2022, p. 77, 97.
On correlation of the 3-fold divisor function with itself - David T. Nguyen, arXiv: 2206.05877 [math.NT], Jun 13 2022, p. 39, OEIS A256392.
Components and Cycles of Random Mappings - Steven Finch, arXiv: 2205.05579 [math.CO], May 11 2022, p. 13, OEIS A001865, A060281, A065456, A273434.
Counting Various Classes of Tournament Score Sequences - Paul K. Stockmeyer, arXiv: 2202.05238 [math.CO], Jul 20 2022, p. 8, OEIS A000571, A351822.
The asymptotic number of score sequences - Brett Kolesnik, arXiv: 2209.13563 [math.CO], Nov 28 2022, p. 3, 4, OEIS A000571, A351822.
On the enumeration of leaf-labelled increasing trees with arbitrary node-degree - Johannes Wirtz, arXiv: 2211.03632 [q-bio.PE], Nov 07 2022, p. 13, 15, OEIS A256006.
Cyclic independence: Boolean and monotone - Octavio Arizmendi, Takahiro Hasebe, Franz Lehner, arXiv: 2204.00072 [math.PR], Sep 08 2022, p. 33, see Remark 7.14, cited my formula from the OEIS A048286 (2014).
Some D-finite and some possibly D-finite sequences in the OEIS - Manuel Kauers, Christoph Koutschan, arXiv:2303.02793 [cs.SC], Mar 05 2023, p. 46.
A unified treatment of families of partition functions - Lida Ahmadi, Ricardo Gómez Aíza, Mark Daniel Ward, arXiv:2303.02240 [math.CO], Mar 03 2023.
Cyclotomic generating functions - Sara C. Billey, Joshua P. Swanson, arXiv:2305.07620 [math.CO], May 12 2023, p. 25, OEIS A120963.
Exact coefficients of finite-size corrections in the Ising model with Brascamp-Kunz boundary conditions and their relationships for strip and cylindrical geometries - Nikolay Sh.Izmailian, Ralph Kenna, Vladimir V. Papoyan, arXiv:2303.03484 [cond-mat.stat-mech], Mar 06 2023, p. 24, OEIS A012495.
Some D-Finite and Some Possibly D-Finite Sequences in the OEIS - Manuel Kauers, Christoph Koutschan, Journal of Integer Sequences, Vol. 26 (2023), Article 23.4.5, p. 39.
Series of the form Sum {a_n*binomial(2n, n)} - Amrik Singh Nimbran and Paul Levrie, Math. Student (2023) Vol. 92, Nos. 3-4, 155-173. Cited my formulas for OEIS A038348 (4.3., p.164) and A096914 (4.2., p.163), without mentioning my name.
Stanley-Wilf Limits for Patterns in Rooted Labeled Forests - Michael Ren, arXiv:2310.02499 [math.CO], Oct 04 2023, p. 11, OEIS A000262.
The Comma Sequence: A Simple Sequence With Bizarre Properties - Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, David W. Wilson, arXiv:2401.14346 [math.NT], Jan 25 2024, p. 12-13, 18, OEIS A368363.
Entropy of axial product of multiplicative subshifts - Jung-Chao Ban, Wen-Guei Hu, Guan-Yu Lai, Lingmin Liao, arXiv:2402.19324 [math.DS], 29 Feb 2024, p. 13, OEIS A023359.
A note on the exact formulas for certain $2$-color partitions - Russelle Guadalupe, arXiv:2404.02367 [math.CO], Apr 02 2024, p. 3, 8, OEIS A002513.
General protocols for the efficient distillation of indistinguishable photons - Jason Saied, Jeffrey Marshall, Namit Anand, Eleanor G. Rieffel, arXiv:2404.14217 [quant-ph], Apr 22 2024, p. 14, 27, 38-39, OEIS A277458.
An exceptional convolutional recurrence - Steven R. Finch, arXiv:2408.12440 [math.CO], Aug 22 2024, p. 2, 4, 12, 13, OEIS A094199.
Tree-tubings and the combinatorics of resurgent Dyson-Schwinger equations - Michael Borinsky, Gerald V. Dunne, Karen Yeats, arXiv:2408.15883 [math-ph], Aug 28 2024, p.13, OEIS A088716, without mentioning my name (I calculated the constant S back in 2014, i.e. 10 years before).
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, second edition - PDF (43 MB), 866 pages, 2310 diagrams, 54 tables, 88 graphs, Dec 20 2017
vol.9 Records in five-man fairy helpmates - PDF (0,5 MB), 61 pages, 196 helpmates, 392 diagrams, 14 tables, Oct 14 2013
vol.10 360 fairy echoes 2012-2024 - PDF (9 MB), 390 pages, 360 chess problems, Aug 07 2024
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)
