Results 21 to 30 of about 149,574 (327)
Note on r-central Lah numbers and r-central Lah-Bell numbers
AIMS Mathematics, 2022 The r-Lah numbers generalize the Lah numbers to the r-Stirling numbers in the same sense. The Stirling numbers and the central factorial numbers are one of the important tools in enumerative combinatorics. The r-Lah number counts the number of partitions
Hye Kyung Kim
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Extended Bernoulli and Stirling matrices and related combinatorial identities [PDF]
, 2013 In this paper we establish plenty of number theoretic and combinatoric identities involving generalized Bernoulli and Stirling numbers of both kinds. These formulas are deduced from Pascal type matrix representations of Bernoulli and Stirling numbers ...
Can, Mümün, Dağlı, M. Cihat
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Congruences for the Stirling numbers and associated Stirling numbers [PDF]
Acta Arithmetica, 1990 Let s(n,k) and S(n,k) be the Stirling numbers of the first and second kind, respectively. The author proves that if \(k+n\) is odd, then \[ s(n,k)\equiv 0 (mod\left( \begin{matrix} n\\ 2\end{matrix} \right)),\quad S(n,k)\equiv 0 (mod\left( \begin{matrix} k+1\\ 2\end{matrix} \right)).
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On partitions, surjections, and Stirling numbers [PDF]
Bulletin of the Belgian Mathematical Society - Simon Stevin, 1994 It is proved that if \(S(m,n)\) denotes the Stirling number of the second kind then \[ S(m, m- k)= \sum^{k-1}_{h= 0} a_{hk}\begin{pmatrix} m\\ k+ h+ 1\end{pmatrix}, \] where the \(a_{hk}\) are positive integers, independent of \(m\), given inductively by \[ a_{0k}= 1\quad\text{and}\quad a_{hk}= \sum^{k-1}_{ j= h} \begin{pmatrix} k+ h\\ j+ h\end{pmatrix}
Hilton, P. (author) +2 more
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G3: Genes, Genomes, Genetics, 2020 Ewen’s sampling formula is a foundational theoretical result that connects probability and number theory with molecular genetics and molecular evolution; it was the analytical result required for testing the neutral theory of evolution, and has since ...
Swaine L. Chen, Nico M. Temme
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Journal of Combinatorial Theory, Series A, 2013 17 pages, 3 ...
Wolfgang Gawronski +3 more
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Stirling Numbers of Uniform Trees and Related Computational Experiments
Algorithms, 2023 The Stirling numbers for graphs provide a combinatorial interpretation of the number of cycle covers in a given graph. The problem of generating all cycle covers or enumerating these quantities on general graphs is computationally intractable, but recent
Amir Barghi, Daryl DeFord
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Energy Reports, 2023 The working gas type had an important effect on the heat transfer performance of the turbulence device in the heater of Stirling engine, but the related researches were scarce, especially under the oscillatory flow.
Feng Xin +4 more
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Discrete Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gloria Olive, Raymond Scurr
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Negative $q$-Stirling numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The notion of the negative $q$-binomial was recently introduced by Fu, Reiner, Stanton and Thiem. Mirroring the negative $q$-binomial, we show the classical $q$ -Stirling numbers of the second kind can be expressed as a pair of statistics on a subset of restricted growth words. The resulting expressions are polynomials in $q$ and $(1+q)$.
Cai, Yue, Readdy, Margaret
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