0-Hecke Algebra Action on the Stanley-Reisner Ring of the Boolean Algebra

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We define an action of the 0-Hecke algebra of type A on the Stanley-Reisner ring of the Boolean algebra. By studying this action we obtain a family of multivariate noncommutative symmetric functions, which specialize to the noncommutative Hall-Littlewood symmetric functions and their (q, t)-analogues introduced by Bergeron and Zabrocki, and to a more general family of noncommutative symmetric functions having parameters associated with paths in binary trees introduced recently by Lascoux, Novelli, and Thibon. We also obtain multivariate quasisymmetric function identities, which specialize to results of Garsia and Gessel on generating functions of multivariate distributions of permutation statistics.

Original languageEnglish (US)
Pages (from-to)293-323
Number of pages31
JournalAnnals of Combinatorics
Volume19
Issue number2
DOIs
Publication statusPublished - Jun 18 2015

    Fingerprint

Keywords

  • 0-Hecke algebra
  • Boolean algebra
  • Stanley-Reisner ring
  • multivariate quasisymmetric function
  • noncommutative Hall-Littlewood symmetric function

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this