Results 1 to 10 of about 4,691 (197)
Elliptic rook and file numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 In this work, we construct elliptic analogues of the rook numbers and file numbers by attaching elliptic weights to the cells in a board. We show that our elliptic rook and file numbers satisfy elliptic extensions of corre- sponding factorization ...
Michael J. Schlosser, Meesue Yoo
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Dirichlet series and series with Stirling numbers
Cubo, 2023 This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers, derangement numbers ...
Khristo Boyadzhiev
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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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Degenerate Derangement Polynomials and Numbers
Fractal and Fractional, 2021 In this paper, we consider a new type of degenerate derangement polynomial and number, which shall be called the degenerate derangement polynomials and numbers of the second kind.
Minyoung Ma, Dongkyu Lim
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Combinatorial Models of the Distribution of Prime Numbers
Mathematics, 2021 This work is divided into two parts. In the first one, the combinatorics of a new class of randomly generated objects, exhibiting the same properties as the distribution of prime numbers, is solved and the probability distribution of the combinatorial ...
Vito Barbarani
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On the p-adic properties of Stirling numbers of the first kind [PDF]
Acta Mathematica Hungarica, 2020 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 $s(n,k)$
Hong, S. F., Qiu, M.
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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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Demonstratio Mathematica, 2022 In this article, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the light of ...
Qi Feng
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On the p-adic valuation of stirling numbers of the first kind [PDF]
Acta Mathematica Hungarica, 2016 For all integers $n \geq k \geq 1$, define $H(n,k) := \sum 1 / (i_1 \cdots i_k)$, where the sum is extended over all positive integers $i_1 < \cdots < i_k \leq n$. These quantities are closely related to the Stirling numbers of the first kind by the identity $H(n,k) = s(n + 1, k + 1) / n!$.
LEONETTI, Paolo, SANNA, CARLO
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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.
Qiu, Min, Hong, Shaofang
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