0-hecke algebra action on the stanley-reisner ring of the boolean algebra

Research output: Contribution to journalConference article

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. We also obtain multivariate quasisymmetric function identities, which specialize to a result of Garsia and Gessel on the generating function of the joint distribution of five permutation statistics.

Original languageEnglish (US)
Pages (from-to)11-22
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2014
Event26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 - Chicago, United States
Duration: Jun 29 2014Jul 3 2014

Keywords

  • 0-Hecke algebra
  • Boolean algebra
  • Multivariate quasisymmetric function
  • Noncommutative Hall-Littlewood symmetric function
  • Stanley-Reisner ring

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Discrete Mathematics and Combinatorics

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