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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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Extended Bell and Stirling numbers from hypergeometric exponentiation [PDF]
, 2001 Exponentiating the hypergeometric series 0FL(1,1,...,1;z), L = 0,1,2,..., furnishes a recursion relation for the members of certain integer sequences bL(n), n = 0,1,2,....
A. I. Extended Bell +6 more
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Combinatorial approach to generalized Bell and Stirling numbers and boson normal ordering problem [PDF]
Journal of Mathematical Physics, 2005 We consider the numbers arising in the problem of normal ordering of expressions in canonical boson creation and annihilation operators. We treat a general form of a boson string which is shown to be associated with generalizations of Stirling and Bell ...
Bergeron F. +6 more
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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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