On the Problem of Uniqueness for the Maximum Stirling Number(s) of the Second Kind
, 2002 Say that an integer n is exceptional if the maximum Stirling number of the second kind S(n, k) occurs for two (of necessity consecutive) values of k. We prove that the number of exceptional integers less than or equal to x is O(x3/5+e), for any e> 0.
Canfield, E. Rodney, Pomerance, Carl
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On degenerate multi-poly-derangement polynomials and numbers
Applied Mathematics in Science and EngineeringThe problem of counting derangements was begun in 1708 by Pierre R[Formula: see text]mond de Montmort (see [Carlitz. The number of derangements of a sequence with given specification. Fibonacci Quart. 1978;16:255–258], [Clarke and Sved.
Sang Jo Yun, Jin-Woo Park
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The Hadamard product of series with Stirling numbers of the second kind and other special numbers [PDF]
Electronic Journal of Mathematics, 2022 Khristo N. Boyadzhiev, Robert Frontczak
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Stirling numbers of the second kind
Duke Mathematical Journal, 1958 Moser, L., Wyman, M.
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Three closed forms for convolved Fibonacci numbers
Results in Nonlinear Analysis, 2020 In the paper, by virtue of the Faà di Bruno formula and several properties of the Bell polynomials of the second kind, the author computes higher order derivatives of the generating function of convolved Fibonacci numbers and, consequently, derives three
Feng Qi
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Annihilating polynomials for quadratic forms and Stirling numbers of the second kind
, 2007 Stefan A. G. De Wannemacker
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On some arithmetic properties of polynomial expressions involving Stirling numbers of the second kind [PDF]
, 2003 Martin Klazar, Florian Luca
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Extended degenerate Stirling numbers of the second kind and extended degenerate Bell polynomials
, 2017 Taekyun Kim, Dae San Kim
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A q, r-analogue for the Stirling numbers of the second kind of Coxeter groups of type B [PDF]
, 2022 Eli Bagno, David Garber, Takao Komatsu
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A Unified Proof of Three Combinatorial Identities Related to the Stirling Numbers of the Second Kind [PDF]
Chun-Ying He, Feng Qi
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