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  1. Home > Articles & Issues >
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  3. $0$-Hecke algebra ac ...
Conference paper

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

Jia Huang ORCID (1)
(1) School of Mathematics
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Imported on
November 21, 2016
Published on
December 31, 2013
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Proceedings
DOI
10.46298/dmtcs.2376
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https://about.hal.science/hal-authorisation-v1
National Science Foundation
1001933
Reflection Group Combinatorics
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$0$-Hecke algebra action on the Stanley-Reisner ring of the Boolean algebra

Jia Huang ORCID (1)
(1) School of Mathematics
Abstract
English
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.
French
Nous définissons une action de l’algèbre de Hecke-$0$ de type A sur l’anneau Stanley-Reisner de l’algèbre de Boole. En étudiant cette action, on obtient une famille de fonctions symétriques non commutatives multivariées, qui se spécialisent pour les non commutatives fonctions de Hall-Littlewood symétriques et leur $(q,t)$-analogues introduits par Bergeron et Zabrocki. Nous obtenons également des identités de fonction quasisymmetrique multivariées, qui se spécialisent à la suite de Garsia et Gessel sur la fonction génératrice de la distribution conjointe de cinq statistiques de permutation.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • $0$-Hecke algebra
  • Stanley-Reisner ring
  • Boolean algebra
  • noncommutative Hall-Littlewood symmetric function
  • multivariate quasisymmetric function.
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