Results 1 to 10 of about 3,168 (184)
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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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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The Peak of Noncentral Stirling Numbers of the First Kind [PDF]
International Journal of Mathematics and Mathematical Sciences, 2015 We locate the peak of the distribution of noncentral Stirling numbers of the first kind by determining the value of the index corresponding to the maximum value of the distribution.
Roberto B. Corcino +2 more
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Variations of central limit theorems and Stirling numbers of the first kind [PDF]
Discrete Mathematics Letters, 2023 We construct a new parametrization of double sequences $\{A_{n,k}(s)\}_{n,k}$ between $A_{n,k}(0)= \binom{n-1}{k-1}$ and $A_{n,k}(1)= \frac{1}{n!}\stirl{n}{k}$, where $\stirl{n}{k}$ are the unsigned Stirling numbers of the first kind. For each $s$ we prove a central limit theorem and a local limit theorem.
Bernhard Heim, Markus Neuhauser
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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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A formula relating Bell polynomials and Stirling numbers of the first kind
Enumerative Combinatorics and Applications, 2021 : In this paper, we prove a general convolution formula involving the Bell polynomials and the Stirling numbers of the first kind. Our proof of the formula is algebraic and establishes an equivalent identity involving the associated exponential ...
Mark Shattuck
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Diagonal recurrence relations for the Stirling numbers of the first kind
arXiv: Classical Analysis and ODEs, 2013 In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the first kind. As by-products, the author also recovers three explicit formulas for special values of the Bell polynomials of the second kind.
Feng Qi
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On the $p$-adic properties of Stirling numbers of the first kind [PDF]
Acta Mathematica Hungarica, 2019 Let $n, k$ and $a$ be positive integers. The Stirling numbers of the first kind, denoted by $s(n,k)$, count the number of permutations of $n$ elements with $k$ disjoint cycles. Let $p$ be a prime. In recent years, Lengyel, Komatsu and Young, Leonetti and Sanna, Adelberg, Hong and Qiu made some progress in the study of the $p$-adic valuations of $s(n,k)$
Shaofang Hong, Min Qiu
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2-Adic valuations of Stirling numbers of the first kind [PDF]
International Journal of Number Theory, 2019 Let [Formula: see text] and [Formula: see text] be positive integers. We denote by [Formula: see text] the 2-adic valuation of [Formula: see text]. The Stirling numbers of the first kind, denoted by [Formula: see text], count the number of permutations of [Formula: see text] elements with [Formula: see text] disjoint cycles.
Min Qiu, Shaofang Hong
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Probabilistic degenerate Stirling numbers of the first kind and their applications [PDF]
European Journal of MathematicsLet Y be a random variable whose degenerate moment generating functions exist in some neighborhoods of the origin. The aim of this paper is to study the probabilistic degenerate Stirling numbers of the first kind associated with Y which are constructed from the degenerate cumulant generating function of Y.
Taekyun Kim, Dae San Kim
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