Results 21 to 30 of about 52,395 (273)
On (q, r, w)-Stirling Numbers of the Second Kind
, 2017 In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function.
U. Duran, M. Acikgoz, S. Araci
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Stirling numbers of the second kind
Duke Mathematical Journal, 1958 L. Moser, M. Wyman
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Asymptotics of the Stirling numbers of the second kind revisited
Applicable Analysis and Discrete Mathematics, 2013 Using the Saddle point method and multiseries expansions, we obtain from the generating function of the Stirling numbers of the second kind {n / m} and Cauchy's integral formula, asymptotic results in central and non-central regions. In the central region, we revisit the celebrated Gaussian theorem with more precision. In the region m = n -
Guy Louchard
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An identity for Stirling numbers of the second kind
Kathmandu University Journal of Science, Engineering and Technology, 2018 We obtain an identity satisfied by the Stirling numbers of the second kind.Kathmandu University Journal of Science, Engineering and TechnologyVol. 13, No.
O. Salas-Torres +2 more
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A probabilistic generalization of the Stirling numbers of the second kind [PDF]
Journal of Number Theory, 2018 J. Adell, A. Lekuona
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Asymptotic Representation of Stirling Numbers of the Second Kind
, 1977 The distribution of the Stirling numbers S(n,k) of the second kind with respect to k has been shown to be asymptotically normal near the mode. A new single-term asymptotic representation of S(n,k), more effective for large k, is given here. It is based on Hermite's formula for a divided difference and the use of sectional areas normal to the body ...
Bleick, Willard Evan, Wang, Peter C.C.
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Some Identities Involving $q$-Stirling Numbers of the Second Kind in Type B [PDF]
Electronic Journal of Combinatorics, 2023 The recent interest in type B $q$-Stirling numbers of the second kind prompted us to give a type B analogue of a classical identity connecting the $q$-Stirling numbers of the second kind and Carlitz's major $q$-Eulerian numbers, which turns out to be a ...
Mingda Ding, Jiang Zeng
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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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Degenerate r-truncated Stirling numbers
AIMS Mathematics, 2023 For any positive integer $ r $, the $ r $-truncated (or $ r $-associated) Stirling number of the second kind $ S_{2}^{(r)}(n, k) $ enumerates the number of partitions of the set $ \{1, 2, 3, \dots, n\} $ into $ k $ non-empty disjoint subsets, such that ...
Taekyun Kim, Dae San Kim, Jin-Woo Park
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