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Study on r-truncated degenerate Stirling numbers of the second kind [PDF]
Open Mathematics, 2022 The degenerate Stirling numbers of the second kind and of the first kind, which are, respectively, degenerate versions of the Stirling numbers of the second kind and of the first kind, appear frequently when we study various degenerate versions of some ...
Kim Taekyun, Kim Dae San, Kim Hyekyung
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SOME REMARKS ABOUT STIRLING NUMBERS OF THE SECOND KIND
Human Research in Rehabilitation, 2013 In this paper we give a representation of Stirling numbers of the second kind, we obtain explicit formulas for some cases of Stirling numbers of the second kind and illustrate a method for founding other such formulas.
Ramiz Vugdalić, Fatih Destović
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Some identities related to degenerate Stirling numbers of the second kind [PDF]
Demonstratio Mathematica, 2022 The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and ...
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Mixed r-stirling numbers of the second kind [PDF]
Online Journal of Analytic Combinatorics, 2014 The Stirling number of the second kind \( S(n, k) \) counts the number of ways to partition a set of \( n \) labeled balls into \( k \) non-empty unlabeled cells. We extend this problem and give a new statement of the \( r \)-Stirling numbers of the second kind and \( r \)-Bell numbers.
Daniel Yaqubi +2 more
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On the 2-adic order of Stirling numbers of the second kind and their differences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Let $n$ and $k$ be positive integers, $d(k)$ and $\nu_2(k)$ denote the number of ones in the binary representation of $k$ and the highest power of two dividing $k$, respectively.
Tamás Lengyel
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The 2-adic valuations of Stirling numbers of the second kind [PDF]
International Journal of Number Theory, 2009 In this paper, we investigate the 2-adic valuations of the Stirling numbers S(n, k) of the second kind. We show that v2(S(4i, 5)) = v2(S(4i + 3, 5)) if and only if i ≢ 7 (mod 32). This confirms a conjecture of Amdeberhan, Manna and Moll raised in 2008. We show also that v2(S(2n+ 1, k + 1)) = s2(n) - 1 for any positive integer n, where s2(n) is the sum ...
Shaofang Hong, Jianrong Zhao, Wei Zhao
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Close encounters with the Stirling numbers of the second kind [PDF]
Mathematics Magazine, 2018 19 pages. This is a modified version of the paper published in the Math Magazine (2012)
Khristo N. Boyadzhiev
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Asymptotic Estimates for Second Kind Generalized Stirling Numbers [PDF]
Journal of Applied Mathematics, 2013 Asymptotic formulas for the generalized Stirling numbers of the second kind with integer and real parameters are obtained and ranges of validity of the formulas are established.
Cristina B. Corcino, Roberto B. Corcino
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Multi-Stirling numbers of the second kind
FilomatThe multi-Stirling numbers of the second kind, the unsigned multi-Stirling numbers of the first kind, the multi-Lah numbers and the multi-Bernoulli numbers are all defined with the help of the multiple logarithm, and generalize respectively the Stirling numbers of the second kind, the unsigned Stirling numbers of the first kind, the unsigned Lah ...
Taekyun Kim, Dae San Kim, Hye Jin Kim
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Properties of Stirling Numbers of the Second Kind.
, 1971 The fact that Stirling Numbers of the Second Kind have arisen in various nonrelated fields, from microelectronics to topology, established the need for a more extensive study of the properties of those Stirling numbers. In order to study the properties, new identities and inequalities for Stirling Numbers if the Second Kind must be formed.
Christopher Benjes
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