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A Formula for the Stirling Numbers of the Second Kind
The American Mathematical Monthly, 2020The Stirling number of the second kind S(n, k) is the number of partitions of {1,2,…,n} into k parts and is given by the following explicit formula: (1) S(n,k)=1k!∑j=0k(−1)k−j(kj)jn.
Qiu-Ming Luo, Gao-Wen Xi
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Stirling Numbers of the Second Kind
, 2005Summary. In this paper we define Stirling numbers of the second kind by cardinality of certain functional classes so that S(n, k) = {f where f is function of n, k : f is onto increasing} After that we show basic properties of this number in order to ...
Karol Pąk
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STIRLING NUMBERS OF THE SECOND KIND
, 2017In 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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, 2020
We derive an explicit formula for the Bernoulli polynomials in terms of the Stirling numbers of the second kind valid for all non-negative real arguments.
Sumit Kumar Jha
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We derive an explicit formula for the Bernoulli polynomials in terms of the Stirling numbers of the second kind valid for all non-negative real arguments.
Sumit Kumar Jha
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On the uniformity of the approximation for r-associated Stirling numbers of the second Kind
Contributions Discret. Math., 2020The $r$-associated Stirling numbers of the second kind are a natural extension of Stirling numbers of the second kind. A combinatorial interpretation of $r$-associated Stirling numbers of the second kind is the number of ways to partition $n$ elements ...
H. Connamacher, Julia A. Dobrosotskaya
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Asymptotics of Stirling and Chebyshev‐Stirling Numbers of the Second Kind
Studies in Applied Mathematics, 2014For the classical Stirling numbers of the second kind, asymptotic formulae are derived in terms of a local central limit theorem. The underlying probabilistic approach also applies to the Chebyshev–Stirling numbers, a special case of the Jacobi–Stirling numbers.
Wolfgang Gawronski+2 more
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On equal values of Stirling numbers of the second kind
Applied Mathematics and Computation, 2011Abstract S k n denote the Stirling number of the second kind with parameters k and n , i. e. S k n the number of the partition of n elements into k non-empty sets. We formulate the following conjecture concerning the common values of Stirling numbers: Let 1 a b be fixed integers. Then all the solutions of
Ferenczik, Judit+2 more
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Three Proofs of an Identity Involving Stirling Numbers of the Second Kind
Advances in Applied MathematicsSheila Sundaram obtained an identity between Stirling numbers of the second kind while studying representations of the symmetric group on the homology of rank-selected subposets of subword order.
云龙 杜
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On the Location of the Maximum Stirling Number(s) of the Second Kind [PDF]
The Stirling number of the second kind S(n, k) is the number of ways of partitioning a set of n elements into k nonempty subsets. It is well known that the numbers S(n, k) are unimodal in k, and there are at most two consecutive values K n such that (for fixed n) S(n,K n ) is maximal.
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