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Free quasi-symmetric functions of arbitrary level

Research paper by Jean-Christophe Novelli, Jean-Yves Thibon

Indexed on: 03 Jun '04Published on: 03 Jun '04Published in: Mathematics - Combinatorics



Abstract

We introduce analogues of the Hopf algebra of Free quasi-symmetric functions with bases labelled by colored permutations. As applications, we recover in a simple way the descent algebras associated with wreath products $\Gamma\wr\SG_n$ and the corresponding generalizations of quasi-symmetric functions. Also, we obtain Hopf algebras of colored parking functions, colored non-crossing partitions and parking functions of type $B$.