A polynomial generalization of some associated sequences related to set partitions
type: Item
instance of: scholarly article
title: A polynomial generalization of some associated sequences related to set partitions
zbMATH Open document ID: 1399.11064
author: Toufik Mansour
author: Mark Shattuck
published in: Periodica Mathematica Hungarica
publication date: 2018-03-14T00:00:00Z
review text: The authors introduce a family of polynomials \(w_{m}^{a,b,c,d} (n,k)\) which for different choices of the parameters \(a,b,c,d\) generate different associate sequences of special numbers. Thus, for example, we have \(w_{1}^{0,1,0,1} (n,k)=S(n,k)\), the classical Stirling numbers of the second kind and \(w_{1}^{0,1,1,0} (n,k)\)are the unsigned Stirling numbers of the first kind. Also, \(w_{1}^{0,1,1,1} (n,k)=L(n,k)\) are the Lah numbers. For \(m\geq 1\) one comes to the associated Stirling and Lah numbers. The paper studies various properties of the above polynomials and provides combinatorial interpretations.
reviewed by: Khristo N. Boyadzhiev
Mathematics Subject Classification ID: 11B73
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05A18
zbMATH DE Number: 6850233
zbMATH Keywords: associated Stirling numbers
zbMATH Keywords: polynomial generalization
zbMATH Keywords: associated Lah numbers
zbMATH Keywords: combinatorial identities
MaRDI profile type: Publication
full work available at URL: s10998-017-0209-9
OpenAlex ID: W2747816025
Wikidata QID: Q60692010
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DBLP publication ID: journals/pmh/MansourS17
DOI: 10.1007/S10998-017-0209-9
description: scientific article; zbMATH DE number 6850233