Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions |
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Authors: | Jean-Christophe Novelli |
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Affiliation: | Université Paris-Est, Institut Gaspard Monge, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France |
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Abstract: | We introduce analogs of the Hopf algebra of Free quasi-symmetric functions with bases labeled by colored permutations. When the color set is a semigroup, an internal product can be introduced. This leads to the construction of generalized descent algebras associated with wreath products Γ?Sn and to the corresponding generalizations of quasi-symmetric functions. The associated Hopf algebras appear as natural analogs of McMahon’s multisymmetric functions. As a consequence, we obtain an internal product on ordinary multi-symmetric functions. We extend these constructions to Hopf algebras of colored parking functions, colored non-crossing partitions and parking functions of type B. |
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Keywords: | Noncommutative symmetric functions Descent algebras Quasi-symmetric functions Combinatorial Hopf algebras |
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