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Free quasi-symmetric functions of arbitrary level

Jean-Christophe Novelli·Jean-Yves Thibon
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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 $Γ\wr\SG_n$ 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 $B$.

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Jean-Christophe Novelli, Jean-Yves Thibon. 2004-06-03. Free quasi-symmetric functions of arbitrary level. https://arxiv.org/abs/math/0405597

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