p, q-Stirling numbers and set partition statistics

Michelle Wachs, Dennis White

Research output: Contribution to journalArticle

107 Scopus citations

Abstract

We give bijections on restricted growth functions and rook placements on stairstep Ferrers boards to show that the q-Stirling numbers of the second kind, described by Gould, arise as generating functions for various statistics on set partitions. We also describe a two-variable, p, q-Stirling number which is the generating function for the joint distribution of pairs of statistics.

Original languageEnglish (US)
Pages (from-to)27-46
Number of pages20
JournalJournal of Combinatorial Theory, Series A
Volume56
Issue number1
DOIs
StatePublished - Jan 1991

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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