Results 31 to 40 of about 1,310,996 (291)
Some Identities of Degenerate Bell Polynomials
Mathematics, 2020 The new type degenerate of Bell polynomials and numbers were recently introduced, which are a degenerate version of Bell polynomials and numbers and are different from the previously introduced partially degenerate Bell polynomials and numbers.
Taekyun Kim +3 more
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The Noncentral Version of the Whitney Numbers: A Comprehensive Study
International Journal of Mathematics and Mathematical Sciences, 2016 This paper is a comprehensive study of a certain generalization of Whitney-type and Stirling-type numbers which unifies the classical Whitney numbers, the translated Whitney numbers, the classical Stirling numbers, and the noncentral Stirling (or r ...
Mahid M. Mangontarum +2 more
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Normal ordering of degenerate integral powers of number operator and its applications
Applied Mathematics in Science and Engineering, 2022 The normal ordering of an integral power of the number operator in terms of boson operators is expressed with the help of the Stirling numbers of the second kind. As a ‘degenerate version’ of this, we consider the normal ordering of a degenerate integral
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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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.
Raymond Scurr, Gloria Olive
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Problems for combinatorial numbers satisfying a class of triangular arrays
Lietuvos Matematikos Rinkinys, 2023 Numbers satisfying a class of triangular arrays, defined by a bivariate first-order linear difference equation with linear coefficients, include a wide range of combinatorial numbers: binomial coefficients, Morgan numbers, Stirling numbers of the first ...
Igoris Belovas
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A Note on Some Identities of New Type Degenerate Bell Polynomials
Mathematics, 2019 Recently, the partially degenerate Bell polynomials and numbers, which are a degenerate version of Bell polynomials and numbers, were introduced.
Taekyun Kim +3 more
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Generalized degenerate Stirling numbers arising from degenerate Boson normal ordering
Applied Mathematics in Science and Engineering, 2023 It is remarkable that, in recent years, intensive studies have been done for degenerate versions of many special polynomials and numbers and have yielded many interesting results.
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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Putting the environment at the heart of prosperity & social inclusion: The Stirling Protocol [PDF]
, 2020 Scotland’s Programme for Government 2019-20, Protecting Scotland’s Future, sets out an ambitious target to achieve net-zero greenhouse gas emissions by 2045.
Rogers, John +4 more
core
Journal of Combinatorial Theory, Series A, 1983 AbstractThe equivalence of two classical sums giving the Stirling numbers of first kind results from a joint law for records.
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