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Article Dans Une Revue Discrete Mathematics Année : 2010

Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions

Résumé

We introduce analogs of the Hopf algebra of Free quasi-symmetric functions with bases labelled 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 $\Gamma\wr\SG_n$ 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.

Dates et versions

hal-00823052 , version 1 (16-05-2013)

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Jean-Christophe Novelli, Jean-Yves Thibon. Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions. Discrete Mathematics, 2010, 310 (24), pp.3584-3606. ⟨10.1016/j.disc.2010.09.008⟩. ⟨hal-00823052⟩
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