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Some Generalizations of Quasi-symmetric Functions and Noncommutative Symmetric Functions

In: Formal Power Series and Algebraic Combinatorics

Author

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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)

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.

Suggested Citation

  • Gérard Duchamp & Florent Hivert & Jean-Yves Thibon, 2000. "Some Generalizations of Quasi-symmetric Functions and Noncommutative Symmetric Functions," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 170-178, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_15
    DOI: 10.1007/978-3-662-04166-6_15
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