Noncommutative symmetric functions with matrix parameters

We define new families of noncommutative symmetric functions and quasi-symmetric functions depending on two matrices of parameters, and more generally on parameters associated with paths in a binary tree. Appropriate specializations of both matrices then give back the two-vector families of Hivert,...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science 2012-01, Vol.DMTCS Proceedings vol. AR,... (Proceedings), p.515-526
Main Authors: Lascoux, Alain, Novelli, Jean-Christophe, Thibon, Jean-Yves
Format: Article
Language:English
Subjects:
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
Computer Science
Discrete Mathematics
macdonald polynomials
noncommutative symmetric functions
quasi-symmetric functions
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Summary:We define new families of noncommutative symmetric functions and quasi-symmetric functions depending on two matrices of parameters, and more generally on parameters associated with paths in a binary tree. Appropriate specializations of both matrices then give back the two-vector families of Hivert, Lascoux, and Thibon and the noncommutative Macdonald functions of Bergeron and Zabrocki. Nous définissons de nouvelles familles de fonctions symétriques non-commutatives et de fonctions quasi-symétriques, dépendant de deux matrices de paramètres, et plus généralement, de paramètres associés à des chemins dans un arbre binaire. Pour des spécialisations appropriées, on retrouve les familles à deux vecteurs de Hivert-Lascoux-Thibon et les fonctions de Macdonald non-commutatives de Bergeron-Zabrocki.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.3059