Results 1 to 10 of about 2,375 (206)
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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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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Asymptotics of Stirling numbers of the second kind [PDF]
Proceedings of the American Mathematical Society, 1974 This work was partially supported by the Office of Naval Research under Contract Number NR 042-286 at the Naval Postgraduate School.
W. E. Bleick, Peter C. C. Wang
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Probabilistic Stirling Numbers of the Second Kind and Applications [PDF]
Journal of Theoretical Probability, 2020 AbstractAssociated with each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention, however, is focused on applications. Indeed, such numbers describe the moments of sums of i.i.d.
José A. Adell
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Probabilistic multi-Stirling numbers of the second kind associated with random variables [PDF]
Applied Mathematics in Science and EngineeringThis paper investigates a probabilistic extension of the multi-Stirling numbers of the second kind and a ‘poly' version of the probabilistic degenerate Lah-Bell polynomials.
Xiangjing Liu +4 more
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A probabilistic generalization of the Stirling numbers of the second kind [PDF]
Journal of Number Theory, 2018 Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers are provided.
José A. Adell, Alberto Lekuona
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On the Uniqueness Conjecture for the Maximum Stirling Numbers of the Second Kind [PDF]
Results in Mathematics, 2021 The Stirling numbers of the second kind S(n, k) satisfy S(n, 0)<¿<S(n, kn)=S(n, kn+1)>¿>S(n, n).A long standing conjecture asserts that there exists no n= 3 such that S(n, kn) = S(n, kn+ 1). In this note, we give a characterization of this conjecture in terms of multinomial probabilities, as well as sufficient conditions on n ensuring that
José A. Adell, Daniel Cárdenas-Morales
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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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Counting of finite topologies and a dissection of Stirling numbers of the second kind [PDF]
Bulletin of the Australian Mathematical Society, 1975 Certain new combinatorial numbers which arise in the counting of finite topologies are introduced and formulae obtained. These numbers are used to obtain a known formula for tn, the number of labelled topologies on n points in terms of the Stirling numbers S(n, p) and dn, the number of labelled T0-topologies on n points. The numbers dn are computed for
V. Krishnamurthy
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Close Encounters with the Stirling Numbers of the Second Kind [PDF]
Mathematics Magazine, 2012 19 pages. This is a modified version of the paper published in the Math Magazine (2012)
Khristo N. Boyadzhiev
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