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Dickson–Stirling numbers [PDF]
Proceedings of the Edinburgh Mathematical Society, 1997 The Dickson polynomialDn, (x,a) of degreenis defined bydenotes the greatest integer function. In particular, we defineD0(x,a) = 2 for all realxanda. By using Dickson polynomials we present new types of generalized Stirling numbers of the first and second kinds. Some basic properties of these numbers and a combinatorial application to the enumeration of
Hsu, L. C. +2 more
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Journal of Mathematical Analysis and Applications, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mínguez Ceniceros, Judit +2 more
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Stirling numbers and periodic points [PDF]
Acta Arithmetica, 2021 We introduce the notion of almost realizability, an arithmetic generalization of realizability for integer sequences, which is the property of counting periodic points for some map. We characterize the intersection between the set of Stirling sequences (of both the first and the second kind) and the set of almost realizable sequences.
Miska P, Ward T
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Degenerate $ r $-truncated Stirling numbers
AIMS Mathematics, 2023 <abstract><p>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 each subset contains at least $ r $ elements.
Taekyun Kim, Dae San Kim, Jin-Woo Park
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Discrete Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrews, G.E. +2 more
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Congruences for the Stirling numbers and associated Stirling numbers [PDF]
Acta Arithmetica, 1990 Let s(n,k) and S(n,k) be the Stirling numbers of the first and second kind, respectively. The author proves that if \(k+n\) is odd, then \[ s(n,k)\equiv 0 (mod\left( \begin{matrix} n\\ 2\end{matrix} \right)),\quad S(n,k)\equiv 0 (mod\left( \begin{matrix} k+1\\ 2\end{matrix} \right)).
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Discrete Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Scurr, Raymond, Olive, Gloria
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Congruences for Stirling numbers and Eulerian numbers [PDF]
Acta Arithmetica, 2008 In this paper, we establish some Fleck-Weisman type and Davis-Sun type congruences for the Stirling numbers and the Eulerian numbers.
Cao, Hui-Qin, Pan, Hao
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Discrete Mathematics, 1984 Let \(N(n,m,r)\) denote the number of permutations of \(\{1,\ldots,n\}\) with \(m\) cycles and such that the numbers \(1,\ldots,r\) occur in distinct cycles, and let \({\mathcal N}(n,m,r)\) denote the number of partitions of \(\{1,\ldots,n\}\) into \(m\) non-empty disjoint sets such that \(1,\ldots,r\) are in distinct subsets.
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Closed formulas for special bell polynomials by Stirling numbers and associate Stirling numbers
Publications de l'Institut Mathematique, 2020 We derive two explicit formulas for two sequences of special values of the Bell polynomials of the second kind in terms of associate Stirling numbers of the second kind, give an explicit formula for associate Stirling numbers of the second kind in terms of the Stirling numbers of the second kind, and, consequently, present two explicit ...
Qi, Feng, Lim, Dongkyu
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