Results 1 to 10 of about 30,409 (195)
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 ...
M. A. Méndez, P. Blasiak, K. A. Penson
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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
doaj +5 more sources
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,....
J. M. Sixdeniers +2 more
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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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New type degenerate Stirling numbers and Bell polynomials [PDF]
Notes on Number Theory and Discrete Mathematics, 2022 In this paper, we introduce a new type degenerate Stirling numbers of the second kind and their degenerate Bell polynomials, which is different from degenerate Stirling numbers of the second kind studied so far. We investigate the explicit formula, recurrence relation and Dobinski-like formula of a new type degenerate Stirling numbers of the second ...
Hye Kyung Kim
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Recurrences of Stirling and Lah numbers via second kind Bell polynomials [PDF]
Discrete Mathematics Letters, 2020 Summary: In the paper, by virtue of several explicit formulas for special values and a recurrence of the Bell polynomials of the second kind, the authors derive several recurrences for the Stirling numbers of the first and second kinds, for 1-associate Stirling numbers of the second kind, for the Lah numbers, and for the binomial coefficients.
Feng Qi +2 more
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Refinements of the Bell and Stirling numbers [PDF]
Transactions on Combinatorics, 2017 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, restricted Bell, and $r$-derangement numbers (and probably more!).
Tanay Wakhare
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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
doaj +2 more sources
Heterogeneous Stirling numbers and heterogeneous Bell polynomials [PDF]
Russian Journal of Mathematical PhysicsThis paper introduces a novel generalization of Stirling and Lah numbers, termed ``heterogeneous Stirling numbers," which smoothly interpolate between these classical combinatorial sequences. Specifically, we define heterogeneous Stirling numbers of the second and first kinds, demonstrating their convergence to standard Stirling numbers for lambda=0 ...
Taekyun Kim, Dae San Kim
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On a New Family of Generalized Stirling and Bell Numbers [PDF]
The Electronic Journal of Combinatorics, 2011 A new family of generalized Stirling and Bell numbers is introduced by considering powers $(VU)^n$ of the noncommuting variables $U,V$ satisfying $UV=VU+hV^s$. The case $s=0$ (and $h=1$) corresponds to the conventional Stirling numbers of second kind and Bell numbers.
Toufik Mansour +2 more
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