Eulerian quasisymmetric functions and cyclic sieving

Bruce Sagan, John Shareshian, Michelle L. Wachs

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

It is shown that a refined version of a q-analogue of the Eulerian numbers together with the action, by conjugation, of the subgroup of the symmetric group Sn generated by the n-cycle (1,2,...,n) on the set of permutations of fixed cycle type and fixed number of excedances provides an instance of the cyclic sieving phenomenon of Reiner, Stanton and White. The main tool is a class of symmetric functions recently introduced in work of two of the authors.

Original languageEnglish (US)
Pages (from-to)536-562
Number of pages27
JournalAdvances in Applied Mathematics
Volume46
Issue number1-4
DOIs
StatePublished - Jan 1 2011

Keywords

  • Cyclic sieving
  • Excedance
  • Major index
  • Quasisymmetric functions

ASJC Scopus subject areas

  • Applied Mathematics

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