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The q-Stirling numbers of the second kind and its applications
Journal of Nonlinear Sciences and Applications, 2018 Summary: The study of \(q\)-Stirling numbers of the second kind began with \textit{L. Carlitz} [Duke Math. J. 15, 987--1000 (1948; Zbl 0032.00304)]. Following Carlitz, we derive some identities and relations related to \(q\)-Stirling numbers of the second kind which appear to be either new or else new ways of expressing older ideas more comprehensively.
Min-Soo Kim, Daeyeoul Kim
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Computing a family of probabilistic numbers in terms of probabilistic Stirling numbers of the second kind [PDF]
Applied Mathematics in Science and EngineeringIn this paper, we introduce the probabilistic Bernoulli numbers, Cauchy numbers, and Euler numbers of order α associated with the random variable Y, utilizing the generating function approach.
Aimin Xu
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The Lucas congruence for Stirling numbers of the second kind [PDF]
Acta Arithmetica, 2000 Let \(\{{t \atop s}\}\) for not negative natural numbers \(t, s\) denote the Stirling number of the second kind. In the note under review the authors shows how to compute the Stirling number modulo \(p\) if one knows the \(p\)-adic expansions of \(s\) and \(t\).
Roberto Sánchez-Peregrino
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ON 2-ADIC ORDERS OF STIRLING NUMBERS OF THE SECOND KIND [PDF]
, 2005 We prove that for any k = 1,... , 2n the 2-adic order of the Stirling number S(2n, k) of the second kind is exactly d(k) − 1, where d(k) denotes the number of 1’s among the binary digits of k. This confirms a conjecture of Lengyel.
Stefan De Wannemacker
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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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Annihilating Polynomials and Stirling Numbers of the Second Kind
Irish Mathematical Society Bulletin, 2006 Stefan A. G. De Wannemacker
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Some identities involving degenerate Stirling numbers arising from normal ordering
AIMS Mathematics, 2022 In this paper, we derive some identities and recurrence relations for the degenerate Stirling numbers of the first kind and of the second kind, which are degenerate versions of the ordinary Stirling numbers of the first kind and of the second kind.
Taekyun Kim, Dae San Kim , Hye Kyung Kim
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New approach to λ-Stirling numbers
AIMS Mathematics, 2023 The aim of this paper is to study the $ \lambda $-Stirling numbers of both kinds, which are $ \lambda $-analogues of Stirling numbers of both kinds. These numbers have nice combinatorial interpretations when $ \lambda $ are positive integers.
Dae San Kim +2 more
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Stirling numbers of the second kind and Bonferroni's inequalities
Elemente der Mathematik, 2005 Horst Wegner
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