Some identities involving degenerate Stirling numbers arising from normal ordering [PDF]
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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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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A Faster and More Accurate Algorithm for Calculating Population Genetics Statistics Requiring Sums of Stirling Numbers of the First Kind [PDF]
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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Normal ordering associated with λ-Stirling numbers in λ-shift algebra [PDF]
Demonstratio Mathematica, 2023 It is known that the Stirling numbers of the second kind are related to normal ordering in the Weyl algebra, while the unsigned Stirling numbers of the first kind are related to normal ordering in the shift algebra.
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae–Stirling numbers [PDF]
Advances in Difference Equations, 2020 The aim of this paper is to study Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae–Stirling numbers of the first and second kinds.
Taekyun Kim +3 more
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Study on r-truncated degenerate Stirling numbers of the second kind [PDF]
Open Mathematics, 2022 The degenerate Stirling numbers of the second kind and of the first kind, which are, respectively, degenerate versions of the Stirling numbers of the second kind and of the first kind, appear frequently when we study various degenerate versions of some ...
Kim Taekyun, Kim Dae San, Kim Hyekyung
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Generalized degenerate Stirling numbers arising from degenerate Boson normal ordering [PDF]
Applied Mathematics in Science and Engineering, 2023 It is remarkable that, in recent years, intensive studies have been done for degenerate versions of many special polynomials and numbers and have yielded many interesting results.
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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Multi-Lah numbers and multi-Stirling numbers of the first kind [PDF]
Advances in Difference Equations, 2021 In this paper, we introduce multi-Lah numbers and multi-Stirling numbers of the first kind and recall multi-Bernoulli numbers, all of whose generating functions are given with the help of multiple logarithm.
Dae San Kim +4 more
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Restricted $r$-Stirling Numbers and their Combinatorial Applications [PDF]
, 2018 We study set partitions with $r$ distinguished elements and block sizes found in an arbitrary index set $S$. The enumeration of these $(S,r)$-partitions leads to the introduction of $(S,r)$-Stirling numbers, an extremely wide-ranging generalization of ...
Beáta Bényi +3 more
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Asymptotic Estimates for Second Kind Generalized Stirling Numbers [PDF]
Journal of Applied Mathematics, 2013 Asymptotic formulas for the generalized Stirling numbers of the second kind with integer and real parameters are obtained and ranges of validity of the formulas are established.
Cristina B. Corcino, Roberto B. Corcino
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