Results 1 to 10 of about 2,551 (257)

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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Asymptotics of the Stirling numbers of the first kind revisited: A saddle point approach [PDF]

Discrete Mathematics & Theoretical Computer Science, 2010
Using the saddle point method, we obtain from the generating function of the Stirling numbers of the first kind [n j] and Cauchy's integral formula, asymptotic results in central and non-central regions.
Guy Louchard
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Variations of central limit theorems and Stirling numbers of the first kind [PDF]

Discrete Mathematics Letters, 2023
Bernhard Heim, Markus Neuhauser
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A formula relating Bell polynomials and Stirling numbers of the first kind

Enumerative Combinatorics and Applications, 2021
Mark Shattuck
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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, Hye Kyung Kim , Taekyun 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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Note on the Higher-Order Derivatives of the Hyperharmonic Polynomials and the r-Stirling Polynomials of the First Kind

Axioms, 2022
In this paper, we focus on the higher-order derivatives of the hyperharmonic polynomials, which are a generalization of the ordinary harmonic numbers. We determine the hyperharmonic polynomials and their successive derivatives in terms of the r-Stirling ...
José L. Cereceda
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Normal ordering associated with λ-Stirling numbers in λ-shift algebra

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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Study on r-truncated degenerate Stirling numbers of the second kind

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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