Some Generalizations of Quasi-symmetric Functions and Noncommutative Symmetric Functions

Gérard Duchamp (), Florent Hivert () and Jean-Yves Thibon ()
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Gérard Duchamp: Université de Rouen, Laboratoire d'Informatique Fondamentale et Appliquée de Rouen — Faculté des Sciences
Florent Hivert: Université de Marne-la-Vallée, Institut Gaspard Monge
Jean-Yves Thibon: Université de Marne-la-Vallée, Institut Gaspard Monge

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 170-178 from Springer

Abstract: Abstract In this paper, we investigate various kinds of generalisations of symmetric functions. The classical algebra Sym of symmetric functions is embedded in QSym, the algebra of quasi-symmetric functions, and is also a quotient of the algebra Sym of noncommutative symmetric functions. A q-analogue QSym q of the algebra QSym provides a kind of unification of both generalizations QSym and Sym of Sym. In this paper we introduce some further genarlizations whose natural bases are various combinatorial objects like standard tableaux, permutations or integer matrices.

Keywords: Hopf Algebra; Symmetric Function; Grothendieck Group; Standard Tableau; Convolution Algebra (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04166-6_15

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DOI: 10.1007/978-3-662-04166-6_15

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