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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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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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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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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The 2-adic valuations of Stirling numbers of the first kind [PDF]
International Journal of Number Theory, 2018 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, Yulu Feng
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The 3-adic valuations of Stirling numbers of the first kind [PDF]
, 2021 Let $n$ and $k$ be positive integers. The Stirling number of the first kind, denoted by $s(n,k)$, counts the number of permutations of $n$ elements with $k$ disjoint cycles. Let $p$ be a prime number and denote by $v_p(n)$ the $p$-adic valuation of $n$.
Min Qiu, Yulu Feng, Shaofang Hong
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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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Moment Generating Stirling Numbers of the first kind and Applications [PDF]
, 2023 In this paper we introduce and investigate moment generating Stirling numbers of the first kind, "`MSN1"'. They are inverses of MSN2's, which make the representation of the moments for a lot of statistical distributions in closed formulas possible. Both MSN1's and MSN2's are related to the r-Stirling numbers, and extend their properties to any real ...
Ludwig Frank
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Tables of the Generalized Stirling Numbers of the First Kind [PDF]
Journal of the ACM, 1964 The generalized Stirling numbers of the first kind are defined, certain of their basic properties are discussed, and tables are given for the square grid k = 0(1)10 and j = 0(1)10 with l = -10(1)10.
William F. Pickard
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On the p-adic valuation of stirling numbers of the first kind [PDF]
Acta Mathematica Hungarica, 2016 12 pages, 3 ...
P. Leonetti, C. Sanna
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