Selected publications and other information

  1. On the p-adic properties of 2-sected sums involving binomial coefficients, p-Adic Numbers, Ultrametric Analysis and Applications 15:1(2023), 23–47, file
  2. New results on the p-adic valuation of Stirling numbers, INTEGERS, Electronic Journal of Combinatorial Number Theory 22(2022), A82, 1-44 (local copy) (with Arnold Adelberg)
  3. Zeckendorf's theorem using indices in an arithmetic progression, Fibonacci Quarterly 59:4(2021), 327-337 (local copy) (with Amelia Gilson, Hadley Killen, Steven J. Miller, Nadia Razek, Joshua M. Siktar, and Liza Sulkin, Williams College, Carnegie Mellon University, and The University of Tennessee-Knoxville, Knoxville)
  4. Divisibility properties of some curiously defined sequences, Journal of Combinatorics and Number Theory 12:1(2021), 35-49 (local copy)
  5. On some p-adic properties and supercongruences of Delannoy and Schröder numbers, INTEGERS, Electronic Journal of Combinatorial Number Theory 20 (2021), A86, 1-20 (local copy)
  6. A note on a subtraction-transfer game, INTEGERS, Electronic Journal of Combinatorial Number Theory 20((2020), G6, 1-8 (local copy)
  7. On p-adic properties of some Fibonacci and Lucas numbers, INTEGERS, Electronic Journal of Combinatorial Number Theory 19(2019), A63, 1-26 (local copy)
  8. A note on a permutation statistic, Journal of Integer Sequences 22(2019), Article 19.5.1 (local copy: pdf)
  9. How to find your soulmate: Set your goal vs. aim at dating sites, Elemente der Mathematik 73(2018), 170-178 (local copy: pdf)
  10. Supercongruences for some lacunary sums of powers of binomial coefficients, International Journal of Number Theory 14:8(2018), 2155-2164, doi:10.1142/S1793042118501294 (local copy: pdf)
  11. Arithmetic properties of lacunary sums of binomial coefficients, INTEGERS, Electronic Journal of Combinatorial Number Theory 18(2018), A6, 1-13 (local copy)
  12. On the rate of p-adic convergence of alternating sums of powers of binomial coefficients, Proceedings of the 17th International Conference on Fibonacci Numbers and Their Applications, Eds. C. Ballot, P. Anderson and T. Komatsu, The Fibonacci Quarterly 55:5(2017), 96-104, (local copy: pdf)
  13. On some lacunary sums of even powers of binomial coefficients, International Journal of Number Theory 13:9(2017), 2381-2392, doi: 10.1142/S1793042117501305 (local copy: pdf)
  14. On the rate of p-adic convergence of sums of powers of binomial coefficients, International Journal of Number Theory 13:8(2017), 2075-2091, doi: 10.1142/S1793042117501111 (local copy: pdf)
  15. The 2-adic order of some generalized Fibonacci numbers, INTEGERS, Electronic Journal of Combinatorial Number Theory 17(2017), A5, 1-10 (local copy: pdf) (with Diego Marques)
  16. Order statistics and the length of the best-n-of-(2n-1) competition, Communications in Statistics--Theory and Methods 46(2017), 406-414, doi: 10.1080/03610926.2014.995822 (local copy: pdf)
  17. On p-adic properties of the Stirling numbers of the first kind, Journal of Number Theory 148(2015), 73–94, doi: 10.1016/j.jnt.2014.09.015 (local copy: pdf)
  18. The 2-adic order of the Tribonacci numbers and the equation Tn = m!, Journal of Integer Sequences 17(2014), Article 14.10, 1-8 (local copy: pdf)  (with Diego Marques)
  19. Stirling numbers of the second kind, associated Stirling numbers of the second kind, and Newton-Euler sequences, Journal of Combinatorics and Number Theory 6(2014), 51-61, (local copy: pdf)
  20. Exact p-adic orders for differences of Motzkin numbers, International Journal of Number Theory 10:3(2014), 653-667, doi:10.1142/S1793042113501157, (local copy: pdf)
  21. On the least significant p-adic digits of certain Lucas numbers, INTEGERS, Electronic Journal of Combinatorial Number Theory 14(2014), A13, 1-15 (local copy: pdf)
  22. On the least significant 2-adic and ternary digits of certain Stirling numbers, INTEGERS, Electronic Journal of Combinatorial Number Theory 13(2013), A47, 1-10 (local copy: pdf)
  23. On divisibility properties of some differences of Motzkin numbers, Annales Mathematicae et Informaticae 41(2013), 121-136 (in Proceedings of the 15th International Conference on Fibonacci Numbers and Their Applications, Institute of Mathematics and Informatics, Eszterházy Károly College, Eger, Hungary, June 25–30, 2012) (local copy: pdf)
  24. On divisibility properties of some differences of the central binomial coefficients and Catalan numbers, INTEGERS, Electronic Journal of Combinatorial Number Theory 13(2013), A10, 1-20 (local copy: pdf)
  25. Revisiting the newsboy problem–optimization with a little help from the airline industry, International Journal of Engineering Management and Economics (IJEME) 2(2012), no. 4, 156-159 (local copy: pdf; final version: pdf, html)
  26. On some 2-adic properties of a recurrence involving Stirling numbers, p-Adic Numbers, Ultrametric Analysis and Applications 4:3(2012), 179-186 (local copy/final version: pdf)
  27. Note on the unbiased estimation of a function of the parameter of the geometric distribution, International Journal of Applied Mathematics and Statistics (IJAMAS) 27(2012), no. 3, html (local copy (preprint): pdf; final version: pdf)
  28. Direct consequences of the basic Ballot Theorem, Statistics & Probability Letters 81(2011), 1476-1481, doi:10.1016/j.spl.2011.05.011 (local copy (preprint): pdf; final version: pdf)
  29. A finite difference approach to counting quadrangles in a circle, Geombinatorics Quarterly 20(2011), no. 4, 168-179 (with Gregory P. Tollisen), (local copy (preprint): pdf)
  30. On approximating point spread distributions, Journal of Statistical Computation and Simulation 81(2011), 1333-1344, doi: 10.1080/00949655.2010.484901 (local copy: pdf, (preprint): pdf)
  31. The Sprague-Grundy function of the real game Euclid, Discrete Mathematics 311 (2011), 457-462 (with Grant Cairns, Nhan Bao Ho), pdf, doi:10.1016/j.disc.2010.12.011 (local copy (preprint): pdf)
  32. Gambler's ruin and winning a series by m games, Annals of the Institute of Statistical Mathematics 63(2011), 181-195, pdf,  doi:10.1007/s10463-008-0214-0 (local copy: pdf)
  33. The distribution of the size of the union of cycles for two types of random permutations, International Journal of Combinatorics, vol. 2010, Article ID751861, 10 pages, 2010, doi:10.1155/2010/751861 (local copy: pdf)
  34. Alternative proofs on the 2-adic order of Stirling numbers of the second kind, INTEGERS, Electronic Journal of Combinatorial Number Theory 10(2010), 453–463 (local copy (preprint): pdf), doi:s10.1515/INTEG.2010.038, also: A38 (local copy: pdf)
  35. On the 2-adic order of Stirling numbers of the second kind and their differences, 21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09, Hagenberg, Austria, Discrete Mathematics and Theoretical Computer Science Proceedings 2009, 561-572, pdf (local copy (preprint): pdf)
  36. The conditional gambler's ruin problem with ties allowed, Applied Mathematics Letters 22(2009), 351-355, preprint, pdf, doi:10.1016/j.aml.2008.04.007
  37. Intermediate and limiting behavior of powers of some circulant matrices, Ars Combinatoria 88(2008), 229-255 (with Gregory P. Tollisen), preprint, dvi/pdf/ps
  38. The game of 3-Euclid, Discrete Mathematics 308(2008), 1130-1136 (with David Collins), pdf (please find the correct Figure 1 here)
  39. On the divisibility of a special power sum, INTEGERS, Electronic Journal of Combinatorial Number Theory 7(2007), A41  (local copy: pdf)
  40. An invariant sum related to record statistics, INTEGERS, Electronic Journal of Combinatorial Number Theory 7(2007), A40 (local copy: pdf)
  41. Asymptotics for lacunary sums of binomial coefficients and a card problem with ranks, Journal of Integer Sequences 10 (2007), Article 07.7.2 (local copy: pdf)
  42. Keeping scores, Journal of Statistical Planning and Inference 137(2007), 2208 – 2213 (with David Collins and Gregory P. Tollisen), preprint, pdf
  43. A counting based proof of the generalized Zeckendorf's theorem, The Fibonacci Quarterly 44(2006), 324-325, preprint, pdf/ps
  44. Identities for the generating function of the multiset [nΦm] for m= -1,1,2, The Fibonacci Quarterly 44(2006), 274-276, preprint, pdf/ps
  45. On calculating the Sprague-Grundy function for the game Euclid, Proceedings of the 11th International Conference on  Fibonacci Numbers and Their Applications, 2004, Congressus Numerantium 194(2009), 167-172, pdf
  46. A congruential identity and the 2-adic order of lacunary sums of binomial coefficients, INTEGERS, Electronic Journal of Combinatorial Number Theory 4(2004), A4 (with Gregory P. Tollisen) (local copy: pdf/dvi)
  47. On minimizing distance by the road less traveled, Elemente der Mathematik 58(2003), 89-107(with Gregory P. Tollisen), pdf, preprint: pdf/dvi/ps with figures (zip)
  48. On the order of lacunary sums of binomial coefficients, INTEGERS, Electronic Journal of Combinatorial Number Theory 3(2003), A3 (local copy: pdf/dvi)
  49. A nim-type game and continued fractions, The Fibonacci Quarterly 41(2003), 310-320, preprint, pdf/dvi/ps
  50. Divisibility properties by multisection, The Fibonacci Quarterly 41(2003), 72-79, preprint, pdf/dvi/ps
  51. Difference equations and divisibility properties of sequences, Journal of Difference Equations and Applications 8(2002), 741-753, pdf, preprint: pdf/dvi/ps
  52. On reaching head to tail ratios for balanced and unbalanced coins, Journal of Statistical Planning and Inference 101(2002), 203-210, pdf, preprint: pdf/dvi/ps
  53. On the order of Stirling numbers and alternating binomial coefficient sums, The Fibonacci Quarterly 39(2001), 444-454 (with Ira Gessel), pdf/dvi/ps
  54. Color switching games, Ars Combinatoria 56(2000), 223-234 (with Gregory P. Tollisen), pdf/dvi/ps
  55. Divisibility properties by recurrence relations, in Advances in Difference Equations, Proceedings of the Second International Conference on Difference Equations and Its Applications, Eds. S. Elaydi, I. Győri, G. Ladas, Gordon and Breach Science Publishers, 1997, 391-397,  pdf/dvi/ps
  56. On the moments of the number of cycles of a random permutation by simple enumeration, Sankhya, Series A, Pt.1, 59(1997), 133-137, pdf, preprint: pdf/dvi/ps
  57. On some properties of the series Σk>=0 kn xk and the Stirling number of the second kind, Special issue in honor of the eightieth birthday of Paul Erdős, Discrete Mathematics 150(1996), 281-292,  pdf, preprint: pdf/dvi/ps
  58. On the probability of reaching a given head to tail ratio, Journal of Combinatorics, Information & System Sciences 20(1995), no. 1-4, 273–278, preprint: pdf/ps
  59. The order of the Fibonacci and Lucas numbers, The Fibonacci Quarterly 33(1995), 234-239, pdf/dvi/ps
  60. Characterizing the 2-adic order of the logarithm, The Fibonacci Quarterly 32(1994), 397-401, pdf/dvi/ps
  61. On the divisibility by 2 of the Stirling numbers of the second kind, The Fibonacci Quarterly 32(1994), 194-201, pdf/dvi/ps
  62. A combinatorial identity and the World Series, SIAM Review 35(1993), 294-297, pdf, preprint: pdf/dvi/ps
  63. A convergence criterion for recurrent sequences with application to the partition lattice, Analysis 12(1992), 109-119 (with László Babai), pdf/dvi/ps
  64. On a recurrence involving Stirling numbers, European Journal of Combinatorics 5(1984), 313-321, pdf
  1. Lengyel's constant, set partitions and Bell numbers, downloaded from the MathSoft site, April 1999, pdf/ps
  2. Lengyel's constant at MathWorld, Wolfram Research, © 1999 CRC Press LLC, © 1999-2003 Wolfram Research, Inc.
  3. Sequence A005121, info based on The Encyclopedia of Integer Sequences, Academic Press, 1995, by N. J. A. Sloane and S. Plouffe (on the decimal expansion: A086053)
  4. Lengyel's constant in CRC Concise Encyclopedia of Mathematics (then "Search in this book" or click on this: p1749) or in one single step: CRC, Second Edition, Chapman & Hall / CRC, 2002, by Eric W. Weisstein
  5. Lengyel's constant in Section 5.7, pp. 316-321, in Mathematical Constants (contents and excerpts), Encyclopedia of Mathematics and its Applications (No. 94), Cambridge University Press, 2003, by Steven R. Finch, pdf/djvu
  6. On the asymptotic analysis of a class of linear recurrences (or see the downloaded local copy: pdf/ps), by Thomas Prellberg, talk given at INRIA, Project Algorithms Seminars, 2002-2003 (with summary by Marni Mishna, in Algorithms Seminar 2002–2004, F. Chyzak (ed.), INRIA, (2005), pp. 47–50); for a longer version please see: On the asymptotic analysis of a class of linear recurrences, talk given at the 14th International Conference on Formal Power Series & Algebraic Combinatorics (FPSAC 2002), Melbourne, Australia, 2002 (downloaded local copy: pdf)
  7. Lengyel's constant at Wolfram Alpha, 2014 (downloaded local copy: htm)
  8. p-adic properties of Lengyel’s numbers, by D. Barsky and J.-P. Bézivin, Journal of Integer Sequences 17(2014), Article 14.7.3, 1-21 (downloaded local copy: pdf)
  9. p-adic properties of recurrences involving Stirling numbers, by N. J. H. Lai, University of Waterloo, Waterloo, Ontario, Canada, 2014, 1-15 (downloaded local copy: pdf)
  10. several other references (including other topics) in The On-Line Encyclopedia of Integer Sequence (OEIS)

References in the On Line Encyclopedia of Integer Sequences

last update:  05/19/2023 by tl