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.
- 0-Hecke algebra
- Boolean algebra
- Stanley-Reisner ring
- multivariate quasisymmetric function
- noncommutative Hall-Littlewood symmetric function
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics