Selected references for Tamas Lengyel
Selected references for Tamas Lengyel
November 22, 2015
1. L. A. Medina and E. S. Rowland, p-regularity of the p-adic valuation of the Fibonacci sequence, Fibonacci Quarterly 53:3(2015), 265-271, arXiv:0910.2907v2, October 2009
2. V. Gurvich and N.B. Ho, On tame, pet, domestic, and miserable impartial games, arXiv:1508.06343v1, August 2015
3. P. Miska, Arithmetic properties of the sequence of derangements and its generalizations, Master thesis prepared at the Institute of Mathematics of Jagiellonian University, Kraków, Poland, arXiv:1508.01987, August 2015
4. R. Dorward, P.L. Ford, E. Fourakis, P.E. Harris, S.J. Miller, E.A. Palsson, and H. Paugh, A generalization of Zeckendorf's theorem via circumscribed m-gons, arXiv:1508.07531v1, August 2015
5. P. Guillot and Y. Ségalat, New congruences for Stirling numbers of the first kind, with an application to Chern classes, arXiv:1507.02834v1, July 2015
6. R. Zulkapli, A.M. Atan and H. Sapar, A method for determining p-adic orders of factorials, Malaysian Journal of Mathematical Sciences 9(2): 277-300 (2015)
7. A. Best, P. Dynes, X. Edelsbrunner, B. McDonald, S.J. Miller, K. Tor, C. Turnage-Butterbaugh, and M. Weinstein, Gaussian distribution of the number of summands in generalized Zeckendorf decompositions in small intervals, arXiv:1501.06833v2, January 2015
8. K. Wójcik, Binomial transform and Dold sequences, Journal of Integer Sequences 18(2015), Article 15.1.1, 1-18
9. N. G. Hamlin, Recurrence Representation, Ph. D. thesis, Department of Mathematics, Washington State University, May 2012, 1-81
10. D. Marques, On generalized Cullen and Woodall numbers that are also Fibonacci numbers, Journal of Integer Sequences 17(2014), Article 14.9.4, 1-11
11. R. Wituła, E. Hetmaniok, and D. Słota, Generalized Gregory’s series, Applied Mathematics and Computation 237(2014), 203-216
12. 2014 MSRI-UP Research Reports, Mathematical Sciences Research Institute, Berkeley, 2014, 1-162
13. A. Roshan, P.H. Jones, and C.D. Greenman, Exact, time-independent estimation of clone size distributions in normal and mutated cells, Journal of the Royal Society, Interface / the Royal Society 10/2014 11(99), 1-13. DOI: 10.1098/rsif.2014.0654
14. P. Pongsriiam, Exact divisibility by powers of the Fibonacci and Lucas numbers, Journal of Integer Sequences 17(2014), Article 14.11.2, 1-12
15. Ph. Demontigny, Th. Do, A. Kulkarni, S.J. Miller, and U. Varma, A generalization of Fibonacci far-difference representations and Gaussian behavior, Fibonacci Quarterly 52:4(2014), 247-273
16. M. Catral, P Ford, P. Harris, S.J. Miller, and D. Nelson, Generalizing Zeckendorf's theorem: the Kentucky sequence, arXiv: 1409.0488v1, September 2014
17. A. Best, P. Dynes, X. Edelsbrunner, B. McDonald, S.J. Miller, K. Tor, C. Turnage-Butterbaugh, and M. Weinstein, Benford behavior of Zeckendorf decompositions, arXiv: 1409.0482v1, September 2014
18. D. Barsky and J.-P. Bézivin, p-adic properties of Lengyel’s numbers, Journal of Integer Sequences 17(2014), Article 14.7.3, 1-21
19. J. Zhao, S. Hong, and W. Zhao, The 2-adic valuations of differences of Stirling numbers of the second kind, arXiv: 1407.8443v1, July 2014
20. S. Park, Arithmetic properties of generalized Fibonacci sequences, arXiv: 1407.8086v1, July 2014
21. F.N. Castro, O.E. Gonzalez, and L.A. Medina, The p-adic valuation of Eulerian numbers: trees and Bernoulli numbers, manuscript, May 2014, 1-19 (submitted to Experimental Mathematics)
22. T. Chen and S. Kiefer, On the total variation distance of labelled Markov chains, arXiv: 1405.2852v1, May 2014; CSL-LICS '14, Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), Article No. 33, ACM New York, NY, USA, 2014
23. I. Ben-Ari and S.J. Miller, A probabilistic approach to generalized Zeckendorf decompositions, arXiv: 1405.2379v1, May 2014, 1-25
24. K. Dutta, On certain invariants of random digraphs and uniform hypergraphs, Ph.D. thesis, Mathematical Sciences, Homi Bhabha National Institute, India, April 2014, 1-123
25. Ch. Gahm, B. Dünnwald, and R. Sahamie, A multi-criteria master production scheduling approach for special purpose machinery, International Journal of Production Economics 149(2014), 89-101
26. T.L. Urban, The effect of playoff series length on the outcome, International Journal of Revenue Management 7:3-4(2013), 183-194
27. Ph. Demontigny, Th. Do, A. Kulkarni, S.J. Miller, D. Moon, and U. Varma, Generalizing Zeckendorf's theorem to f-decompositions, Journal of Number Theory 141(2014), 136-158
28. M. Kanovich, Multiset rewriting over Fibonacci and Tribonacci numbers, Journal of Computer and System Sciences 80:6(2014), 1138-1151
29. A. Bower, R. Insoft, Sh. Li, S.J. Miller, and Ph. Tosteson, The distribution of gaps between summands in generalized Zeckendorf decompositions, arXiv:1402.3912v2, February 2014 and Journal of Combinatorial Theory Series A 135:2(2014), 130-160
30. P.F. Ayuso, J.M. Grau, and A.M. Oller-Marcén, A von Staudt-type formula for ∑z∈Zn[i] zk, arXiv: 1402.0333v2, February 2014 and Monatshefte für Mathematik 178:3(2015), 345-359
31. J. Sondow and E. Tsukerman, The p-adic order of power sums, the Erdős-Moser equation, and Bernoulli numbers, arXiv: 1401.0322v1, January 2014
32. Y. Chen, WZ method and a formula for the partial sum of a binomial series, Acta Mathematicae Applicatae Sinica (Chinese Series) 36:3(2013), 448-453 (in Chinese)
33. J.M. Grau, A.M. Oller-Marcén, and J. Sondow, On the congruence 1m + 2m + ... + mm = n mod m, where n | m, arXiv:1309.7941, December 2013 and Monatshefte für Mathematik 177:3(2014), 421-436
34. J.-R. Zhao, Congruences for Stirling numbers modulo a power of 2, Journal of Sichuan University (Natural Science Edition) 50:6(2013), 10.3969/j.issn.0490-6756.2013.06.007
35. A. Roshan, P.H. Jones, and C.D. Greenman, An exact, time-independent approach to clone size distributions in normal and mutated cells, arXiv:1311.5769, November 2013
36. D. Marques, Sharper upper bounds for the order of appearance in the Fibonacci sequence, Fibonacci Quarterly 51:3(2013), 233-238
37. D. Aharonov and U. Elias, A binomial identity via differential equations, American Mathematical Monthly 120(2013), 462-466
38. D. Marques, J. A. Sellers, James, and P. Trojovský, On divisibility properties of certain Fibonomial coefficients by a prime, Fibonacci Quarterly 51:1(2013), 78–83
39. M. Bolla, Spectral Clustering and Biclustering: Learning Large Graphs and Contingency Tables, Wiley, 2013, 1-292
40. V. Moll, Numbers and Functions: From a Classical-experimental Mathematician's Point of View, Student Mathematical Library, vol. 65, American Mathematical Society, 2012
41. W.V. Li and V.V. Vysotsky, Probabilities of competing binomial random variables, Journal of Applied Probability 49:3(2012), 731-744
42. N.A. McKay and R.J. Nowakowski, Outcomes of partizan Euclid, INTEGERS 12B(2012), Article A9
43. S. Stevic, Application of difference equations in divisibility, Applied Mathematics and Computation 219:4(2012), 2060-2066
44. O. Beckwith, A. Bower, L. Gaudet, R. Insoft, Sh. Li, S.J. Miller, and Ph. Tosteson, The average gap distribution for generalized Zeckendorf decompositions, arXiv:1208.5820v3, December 2012
45. R. Meštrović, A congruence modulo n3 involving two consecutive sums of powers and its applications, arXiv:1211.4570v1, November 2012
46. N.B. Ho, Two variants of Wythoff's game preserving its P-positions, Journal of Combinatorial Theory, Series A 119:6 (2012), 1302-1314
47. J. Zhao, S. Hong, and W. Zhao, Divisibility by 2 of Stirling numbers of the second kind and their differences, arXiv:1209.6284v1, September 2012 and Journal of Number Theory 140(2014), 324-348
48. D. Marques, The order of appearance of powers of Fibonacci and Lucas numbers, Fibonacci Quarterly 50:3(2012), 239-245
49. Y.-C. Hung, Wald's identity for the fair coin-tossing games and some applications, The Open Statistics and Probability Journal 4(2012), 1-4
50. J. Anděl and Š. Hudecová, Variance of the game duration in the gambler’s ruin problem, Statistics and Probability Letters 82(2012), 1750–1754
51. D. Marques and P. Trojovský, On divisibility of Fibonomial coefficients by 3, Journal of Integer Sequences 15(2012), Article 12.6.4, 1-10
52. D. Marques, The order of appearance of product of consecutive Fibonacci numbers, Fibonacci Quarterly 50:2(2012), 132-139
53. N. Hamlin and W. A. Webb, Representing positive integers as a sum of linear recurrence sequences, Fibonacci Quarterly 50:2(2012), 99-105
54. N. B. Ho, Variations of the Game 3-Euclid, International Journal of Combinatorics, Volume 2012 (2012), Article ID 406250, 11 pages
55. C. D. Bennett and E. Mosteig, Congruence classes of 2-adic valuations of Stirling numbers of the second kind, arXiv:1204.6361v1, April 2012
56. G. Cairns and N. B. Ho, Variants of Wythoff's game translating its P-positions, arXiv:1203.2090v2, March 2012
57. A. S. Fraenkel, RATWYT, The College Mathematics Journal 43:2 (2012), 160-164
58. G. Cairns and N. B. Ho, A restriction of Euclid, arXiv:1202.4597v1, February 2012, Bulletin of the Australian Mathematical Society 86:3(2012), 506-509
59. D. Marques, The order of appearance of integers at most one away from Fibonacci numbers, Fibonacci Quarterly 50:1(2012), 36-43
60. References in the On Line Encyclopedia of Integer Sequences:
|2-adic order of the Tribonacci sequence: A248174; |
Motzkin numbers: A001006;
dissimilarity/ultrametric: A005121, A086053, A097906, A131407;
divisibility of Fibonacci Fn by n: A023172, A129066;
2-adic order of Fn: A090740;
coefficients in (1+x)n mod 1+x4: A099586, A099587, A099588, A099589
exponent of highest power of 2 dividing the sum 1n + 2n + ... + nn: A220779
61. J. L. Cereceda Berdiel, Teorema de Faulhaber sobre las sumas de potencias, in El diablo de los números, Sección a cargo de Javier Cilleruelo Mateo, La Gaceta de la RSME (Real Sociedad Matemática Española), 15:1 (2012), 149–169
62. N. B. Ho, Variations of the game 3-Euclid, International Journal of Combinatorics, Volume 2012 (2012), Article ID 406250, 11 pages
63. K. Dutta, D. Mubayi, and C. R. Subramanian, New lower bounds for the independence number of sparse graphs and hypergraphs, SIAM Journal on Discrete Mathematics 26:3(2012), 1134–1147 (and arXiv:1102.4856v1, February 2011)
64. J.-R. Zhao and W. Zhao, The 2-adic valuation of a kind of Stirling number, Journal of Sichuan University (Natural Science Edition) 48:4(2011), 10.3969/j.issn.0490-6756.2011.04.005
65. J.-C. Schlage-Puchta, Regularity of a function related to the 2-adic logarithm, Bulletin of the Belgian Mathematical Society-Simon Stevin 18:2(2011), 375-377
66. G. Cairns and N. B. Ho, Some remarks on end-Nim, International Journal of Combinatorics, Volume 2011 (2011), Article ID 824742, 9 pages
67. V. Gurvich, Miserable and strongly miserable impartial games, RRR 18-2011, November 2011. RUTCOR Research Report, Rutgers University
68. L. Jones, Using Lucas Sequences to generalize a theorem of Sierpiński, Acta Arithmetica 152:3(2012), 307-322. arXiv:1106.2029, June 2011
69. M. Koloğlu, G. S. Kopp, S. J. Miller, and Y. Wang, On the number of summands in Zeckendorf decompositions, Fibonacci Quarterly 49:2(2011), 116-130
70. V. Addona, S. Wagon, and H. Wilf, How to lose as little as possible, Ars Mathematica Contemporanea 4(2011), 29–62
71. S. M. Hashemiparast and M. Sabzevari, The asymmetric n-player gambler’s ruin problem with ties allowed and simulation, Journal of the Korean Statistical Society 40:3(2011), 267-276
72. G. Cairns and N. B. Ho, Min, a combinatorial game having a connection with prime numbers, INTEGERS 10(2010), 765-770
73. O. Y. Chan and D. Manna, Congruences for Stirling numbers of the second kind, in Gems in Experimental Mathematics, American Mathematical Society, Contemporary Mathematics Volume 517, 2010, 97-111
74. K. MacMillan and J. Sondow, Divisibility of power sums and the generalized Erdős-Moser equation, arXiv:1010.2275v2, October 2010
75. S. J. Miller and Y. Wang, From Fibonacci number to central limit type theorems, arXiv:1008.3202v1, August 2010 and Journal of Combinatorial Theory, Series A 119:7(2012), 1398-1413
76. V. H. Moll, Seized opportunities, Notices of the American Mathematical Society 57(2010), 476-484
77. V.I. Pozdnyakov and J.M. Steele, Bugs on a budget: distributed sensing with cost for reporting and non-reporting, Probability in the Engineering and Informational Sciences 24(2010), 525-534
78. M. Stern, Efficiently processing complex queries in sensor networks, Ph.D. thesis, Karlsruhe Insitute of Technology, Karlsruhe, Germany, February 2010 (Doktors der Ingenieurwissenschaften, Fakultät für Informatik des Karlsruher Instituts für Technologie (KIT))
79. X. Chen and R. Lin, A summation formula for the finite sum of the form such as Σf(i)ti, Advanced Computational Intelligence (IWACI), 2010 Third International Workshop, Aug. 2010, 396-398
80. T. W. Cusick, Y. Li, and P. Stănică, On a conjecture for balanced symmetric Boolean functions, Journal of Mathematical Cryptology 3(2009), 1–18
81. S. Hong, J. Zhao, and W. Zhao, The 2-adic valuation of Stirling numbers of the second kind, International Journal of Number Theory 8(2012), 1057–1066, arXiv:0907.3412v1, July 2009
82. M. A. El-Shehawey, On the gambler's ruin problem for a finite Markov chain, Statistics & Probability Letters 79(2009), 1590-1595
83. H. Tanil, Erratum to “An order statistics model based on the list of top m scores after lth change” [J. Statist. Plann. Inference139(2009), 2189–2195], Journal of Statistical Planning and Inference 139(2009), 3392
84. H. Tanil, An order statistics model based on the list of top m scores after lth change, Journal of Statistical Planning and Inference 139(2009), 2189-2195
85. C. Zurnieden, Descriptions of the Algorithms, Pragmatic Mathematical Service, July 29, 2008, 1-159
86. P. Sun, A random walk problem involving generalized binomial series, Journal of Mathematical Research & Exposition 28(2008), 22-24
87. V. H. Moll and D. Manna, A remarkable sequence of integers, Expositiones Mathematicae 27:4(2009), 289-312, arXiv: 0812.3374v1, December 2008
88. M. Stern, E. Buchmann, and K. Böhm, Where in the Sensor Network Should the Join Be Computed, After All? in Proceedings of the First Ubiquitous Knowledge Discovery Workshop (UKD'08), Universitat Karlsruhe, September 2008
89. T. Amdeberhan, D. Manna, V. H. Moll, The 2-adic valuation of a sequence arising from a rational integral, to appear in Journal of Combinatorial Theory, Series A 115(2008), 1474-1486
90. T. Amdeberhan, D. Manna, V. H. Moll, The 2-adic valuation of Stirling numbers, Experimental Mathematics 17(2008), 69–82
91. Singly and doubly even, on 2-adic behavior, Wikipedia, 2008
92. D.M. Davis, Divisibility by 2 and 3 of certain Stirling numbers, INTEGERS 8(2008), #A56, 1-25
93. S. Hofmann, G. Schuster, and J. Steuding, Euclid, Calkin & Wilf: Playing with rationals, Elemente der Mathematik 63(2008), 109 – 117
94. J. Steuding, Eine Einführung in die Diophantische Approximationslehre, QED-Workshop, Würzburg, September 24, 2007; update January 30, 2008, 62 pp.
95. L. Bu and M. L. Fernandez, Spinner, track meet, and probability, Journal of Online Mathematics 7(2007), Article ID 1659
96. M. Stern, Optimal locations for joint processing in sensor networks, Mobile Data Management, 336-340, 2007 International Conference, May 2007
97. P. Winkler, Mathematical Mind-Benders, A.K. Peters, 2007
98. X. Wang and Y. Wu, Minimum light number of lit-only σ-game on a tree, Theoretical Computer Science 381(2007), 292-300
99. S. Hofmann, Kombinatorische Spieltheorie am Beispiel von Nim und Euklid, Thesis, Bayerische Julius-Maximilians-Universität Würzburg, 2007, 1-97
100. V. A. Gurvich, On the misère version of game Euclid and miserable games, Discrete Mathematics 307(2007), 1199-1204
101. P. Paule and C. Schneider, Truncating binomial series with symbolic summation, INTEGERS 7(2007) #A22, 1-9 (also: J. Kepler University, Linz. Technical report no. 2006-42, 2006. SFB-Report)
102. T. W. Cusick, Y. Li, P. Stanica, Balanced symmetric functions over GF(p), IEEE Transactions on Information Theory 54:3(2008), 1034-1037 (also: manuscript, 2006, 1-21)
103. Z.-W. Sun, Fleck quotients and Bernoulli numbers, manuscript, 2006, 1-38
104. S. De Wannemacker, Annihilating polynomials and Stirling numbers of the second kind, Ph.D. thesis, School of Mathematical Sciences, University College Dublin, June 2006, 1-97
105. C. M. Rump, The effects of home-away sequencing on the length of best-of-seven game playoff series, Journal of Quantitative Analysis in Sports 2(2006), 1-18
106. J. Zhu and X. Liu, Existence of positive solutions of systems of Volterra nonlinear difference equations, Nonlinear Oscillations 9(2006), 34-45
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108. G. Della Riccia, Converting between generalized Bell, Lah, Stirling, and Tanh numbers, Journal of Integer Sequences 9(2006), Article 06.3.5
109. A. S. Fraenkel, Euclid and Wythoff games, Discrete Mathematics 304(2005), 65-68
110. S. De Wannemacker, On the 2-adic order of the Stirling numbers of the second kind, INTEGERS 5(2005), #A21, 1-7
111. D. Collins, Variations on a theme of Euclid, INTEGERS 5(2005), #G03, 1-12
112. M. Bolla and A. Krámli, Statisztikai következtetések elmélete, Typotex Kiadó. Budapest, 2005, 1-407 (The theory of statistical inference)
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116. J. Sándor and B. Crstici, Handbook of Number Theory II, Kluwer Academic Publishers / Springer, January 2004
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118. P. J. Larcombe, E. J. Fennessey, W. A. Koepf, and D. R. French, The Catalan numbers re-visit the World Series, Congressus Numerantium 165(2003), 19-32
119. S. R. Finch, Mathematical Constants, on Lengyel’s Constant, Section 5.7, in Constants associated with enumerating discrete structures, Encyclopedia of Mathematics and its Applications 94, Cambridge University Press, May 2003, pp. 316-321
120. F. Luca, On positive numbers n for which Ω(n) divides Fn, Fibonacci Quarterly 41(2003), 365-371
121. J.-P. Allouche and J. Shallit, Automatic Sequences: Theory, Applications, Generalizations, Cambridge University Press, 2003
122. S. R. Finch, Bipartite, k-colorable and k-colored graphs, unpublished note, 2003
123. S. R. Finch, Transitive relations, topologies and partial orders, unpublished note, 2003
124. Th. Prellberg, On the asymptotic analysis of a class of linear recurrences, talk given at INRIA, Project Algorithms Seminars, 2002-2003,
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