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

J. B. Remmel, Michelle L Galloway

Research output: Contribution to journalArticle

26 Citations (Scopus)

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

Fingerprint

Stirling numbers
Q-analogue
Stirling numbers of the first kind
Stirling numbers of the second kind
Generating Function
Permutation
Signed Permutations
Set Partition
Growth Function
Statistics
Non-negative
Integer

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Rook theory, generalized stirling numbers and (p, q)-analogues. / Remmel, J. B.; Galloway, Michelle L.

In: Electronic Journal of Combinatorics, Vol. 11, No. 1 R, 22.11.2004, p. 1-48.

Research output: Contribution to journalArticle

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