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# $0$-Hecke algebra action on the Stanley-Reisner ring of the Boolean algebra

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.
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https://hal.inria.fr/hal-01207589
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Jia Huang. $0$-Hecke algebra action on the Stanley-Reisner ring of the Boolean algebra. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.11-22, ⟨10.46298/dmtcs.2376⟩. ⟨hal-01207589⟩

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