Results 1 to 10 of about 30,307 (185)
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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Combinatorial approach to generalized Bell and Stirling numbers and boson normal ordering problem [PDF]
, 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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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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q-Stirling sequence spaces associated with q-Bell numbers
Open MathematicsIn this study, we build qq-analog of the qq-Stirling matrix involved qq-Bell numbers Sq=(Snk(q)){{\mathbb{S}}}_{q}=({S}_{nk}\left(q)) defined by Sq=(Snk(q))=Sq(n,k)Bq(n),0≤k≤n,0,otherwise.\begin{array}{r}{{\mathbb{S}}}_{q}=({S}_{nk}\left(q))=\left ...
Atabey Koray Ibrahim +3 more
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A formula relating Bell polynomials and Stirling numbers of the first kind
Enumerative Combinatorics and Applications, 2021 Mark Shattuck
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Note on r-central Lah numbers and r-central Lah-Bell numbers
AIMS Mathematics, 2022 The r-Lah numbers generalize the Lah numbers to the r-Stirling numbers in the same sense. The Stirling numbers and the central factorial numbers are one of the important tools in enumerative combinatorics. The r-Lah number counts the number of partitions
Hye Kyung Kim
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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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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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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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