Rook theory, generalized stirling numbers and (p, q)-analogues

J. B. Remmel, Michelle L. Wachs

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

In this paper, we define two natural (p, q)-analogues of the generalized Stirling numbers of the first and second kind S1(α,β,r) and S2(α; β; r) as introduced by Hsu and Shiue [17]. We show that in the case where β = 0 and α and r are nonnegative integers both of our (p; q)-analogues have natural interpretations in terms of rook theory and derive a number of generating functions for them. We also show how our (p; q)-analogues of the generalized Stirling numbers of the second kind can be interpreted in terms of colored set partitions and colored restricted growth functions. Finally we show that our (p; q)-analogues of the generalized Stirling numbers of the first kind can be interpreted in terms of colored permutations and how they can be related to generating functions of permutations and signed permutations according to certain natural statistics.

Original languageEnglish (US)
Pages (from-to)1-48
Number of pages48
JournalElectronic Journal of Combinatorics
Volume11
Issue number1 R
StatePublished - Nov 22 2004

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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