Jia Huang
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$0$-Hecke algebra action on the Stanley-Reisner ring of the Boolean algebra
dmtcs:2376 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2014,
DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
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https://doi.org/10.46298/dmtcs.2376
$0$-Hecke algebra action on the Stanley-Reisner ring of the Boolean algebra
Authors: Jia Huang 1
0000-0002-9439-0067
Jia Huang
1 School of Mathematics
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.