Results 1 to 10 of about 1,852 (188)
On Some Congruences for the Bell Numbers and for the Stirling Numbers
Journal of Number Theory, 1991 AbstractWe shall give some congruences for the Bell numbers, and for the Stirling numbers, by investigating the elementary properties of p-adic integrals.
Tsumura, Hirofumi
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A Combinatorial Model for q-Generalized Stirling and Bell Numbers [PDF]
Discrete Mathematics and 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 Mendez
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AxiomsExplicit formulas for graphical Stirling and Bell numbers are known for relatively few graph families. We derive exact expressions for three classes whose independence structure admits a complete combinatorial description: complete multipartite graphs ...
Julian Allagan
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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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The Relationship of Multiset, Stirling Number, Bell Number, and Catalan Number
Science and Technology Indonesia, 2023 Catalan numbers is not as famous as Fibonacci numbers, however this number has own its beauty and arts. Catalan numbers was discovered by Ming Antu in 1730, however, this numbers is credited to Eugene Catalan when he was studying parentheses in 1838 ...
Wamiliana, Attiya Yuliana, Fitriani
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Q-Stirling Numbers of the Second Kind and q-Bell Numbers for Graphs
Electronic Notes in Discrete Mathematics, 2016 Stirling numbers of the second kind and Bell numbers for graphs were defined by Duncan and Peele in 2009. In a previous paper, one of us, jointly with Nyul, extended the known results for these special numbers by giving new identities, and provided a list of explicit expressions for Stirling numbers of the second kind and Bell numbers for particular ...
Michael J Schlosser
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A Simple Combinatorial Interpretation of Certain Generalized Bell and Stirling Numbers
Discrete Mathematics, 2014 In a series of papers, P. Blasiak et al. developed a wide-ranging generalization of Bell numbers (and of Stirling numbers of the second kind) that appears to be relevant to the so-called Boson normal ordering problem. They provided a recurrence and, more recently, also offered a (fairly complex) combinatorial interpretation of these numbers.
Pavol Hell, Pietro Codara
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Heterogeneous Stirling Numbers and Heterogeneous Bell Polynomials
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 ...
Kim, Taekyun, Kim, Dae San
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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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Probabilistic Heterogeneous Stirling Numbers and Bell Polynomials
Integral Transforms and Special FunctionsLet Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures unify several classical and probabilistic families, including those of Stirling, Lah, Bell and Lah-Bell.
Taekyun Kim
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