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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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On an Identity Involving Stirling Numbers of the Second Kind
European Journal of Mathematics and Statistics, 2023 We investigate two generalized forms for the recurrence relation S(n, k) = kS(n - 1, k) + S(n - 1, k - 1). From these generalized forms, we derive a new identity, for which a proof of the identity is given.
Kwame Yankson
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Annihilating polynomials for quadratic forms and Stirling numbers of the second kind [PDF]
Mathematische Nachrichten, 2007 AbstractWe present a set of generators of the full annihilator ideal for the Witt ring of an arbitrary field of characteristic unequal to two satisfying a non‐vanishing condition on the powers of the fundamental ideal in the torsion part of the Witt ring. This settles a conjecture of Ongenae and Van Geel.
Stefan A. G. De Wannemacker
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Some Properties of the Non-central Stirling Numbers of the Second Kind with Complex Parameters
European Journal of Pure and Applied MathematicsThis work extends the non-central Stirling numbers of the second kind to complex arguments. This extension is achieved through an integral representation employing a Hankel contour.
Erwin Arlan, Maribeth Montero
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Probabilistic Poly Degenerate r-Stirling Numbers of the Second Kind and r-Bell Polynomials
European Journal of Pure and Applied MathematicsWe introduce degenerate poly r-Stirling numbers of the second kind and poly r-Bell polynomials by using degenerate polyexponential function and investigate some properties of these number and polynomials.
S. H. Lee
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Some identities on $λ$-analogues of $r$-stirling numbers of the second kind
European Journal of Pure and Applied Mathematics, 2022 Recently, the λ-analogues of r-Stirling numbers of the first kind were studied by Kim-Kim. The aim of this paper is to introduce the λ-analogues of r-Stirling numbers of the second kind and to investigate some properties, recurrence relations and certain
Dae San Kim, Hye Kyung Kim, Taekyun Kim
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p-adic Stirling numbers of the second kind
The Fibonacci Quarterly, 2013 13 ...
Donald M. Davis
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Multisectioned moments of stirling numbers of the second kind
Journal of Combinatorial Theory, Series A, 1973 The Stirling number of the second kind, S(n, k), enumerates the ways that n distinct objects can be stored in k non-empty indistinguishable boxes. When k is restricted to a given residue class modulo μ, the moments of the distribution S(n, k) have properties associated with the Olivier functions of order μ evaluated at 1 and −1. The simplest example is
D. H. Lehmer
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Strong Asymptotics of the Generating Polynomials of the Stirling Numbers of the Second Kind
Journal of Approximation Theory, 2001 AbstractFor the horizontal generating functions Pn(z)=∑nk=1S(n, k)zk of the Stirling numbers of the second kind, strong asymptotics are established, as n→∞. By using the saddle point method for Qn(z)=Pn(nz) there are two main results: an oscillating asymptotic for z∈(−e, 0) and a uniform asymptotic on every compact subset of C\[−e, 0]. Finally, an Airy
Christian Elbert
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Bounds on the location of the maximum Stirling numbers of the second kind [PDF]
Discrete Mathematics, 2009 Let K_n denote the smaller mode of the nth row of Stirling numbers of the second kind S(n, k). Using a probablistic argument, it is shown that for all n>=2, [exp(w(n))]-2<=K_n<=[exp(w(n))]+1, where [x] denotes the integer part of x, and w(n) is Lambert's W-function.
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