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 language | English (US) |
|---|---|
| Pages (from-to) | 11-22 |
| Number of pages | 12 |
| Journal | Discrete Mathematics and Theoretical Computer Science |
| State | Published - 2014 |
| Externally published | Yes |
| Event | 26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 - Chicago, United States Duration: Jun 29 2014 → Jul 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
- General Computer Science
- Discrete Mathematics and Combinatorics