Results 1 to 10 of about 1,050 (135)
Refinements of the Bell and Stirling numbers [PDF]
Transactions on Combinatorics, 2018 We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associated Bell, incomplete Stirling, restricted factorial ...
Tanay Wakhare
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A Combinatorial Model for $q$-Generalized Stirling and Bell Numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We describe a combinatorial model for the $q$-analogs of the generalized Stirling numbers in terms of bugs and colonies. Using both algebraic and combinatorial methods, we derive explicit formulas, recursions and generating functions for these $q ...
Miguel Méndez, Adolfo Rodríguez
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A formula relating Bell polynomials and Stirling numbers of the first kind
Enumerative Combinatorics and Applications, 2021 Summary: 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 generating function, where we make use of induction, manipulation of finite sums and several ...
Mark Shattuck
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Axioms, 2022 In this paper, we focus on the higher-order derivatives of the hyperharmonic polynomials, which are a generalization of the ordinary harmonic numbers. We determine the hyperharmonic polynomials and their successive derivatives in terms of the r-Stirling ...
José L. Cereceda
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New Properties on Degenerate Bell Polynomials
Complexity, 2021 The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate versions of the Bell numbers and polynomials. We derive some new identities and properties of those numbers and polynomials that are associated with the ...
Taekyun Kim +4 more
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On the Total Positivity and Accurate Computations of r-Bell Polynomial Bases
Axioms, 2023 A new class of matrices defined in terms of r-Stirling numbers is introduced. These r-Stirling matrices are totally positive and determine the linear transformation between monomial and r-Bell polynomial bases.
Esmeralda Mainar +2 more
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The 2-successive partial Bell polynomials [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we discuss a new class of partial Bell polynomials. The first section gives an overview of partial Bell polynomials and their related 2-successive Stirling numbers.
Meriem Tiachachat, Miloud Mihoubi
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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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Some identities related to degenerate Stirling numbers of the second kind
Demonstratio Mathematica, 2022 The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and ...
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Some identities related to degenerate r-Bell and degenerate Fubini polynomials
Applied Mathematics in Science and Engineering, 2023 Many works have been done in recent years as to explorations for degenerate versions of some special polynomials and numbers, which began with the pioneering work of Carlitz on the degenerate Bernoulli and degenerate Euler polynomials.
Taekyun Kim, Dae San Kim, Jongkyum Kwon
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