Journal of Noncommutative Geometry


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Volume 8, Issue 1, 2014, pp. 141–162
DOI: 10.4171/JNCG/151

Published online: 2014-03-20

Polynomial realizations of some combinatorial Hopf algebras

Loïc Foissy[1], Jean-Christophe Novelli[2] and Jean-Yves Thibon[3]

(1) Université de Reims, France
(2) Université de Paris-Est, Marne-la-Vallée, Fance
(3) Université de Paris-Est, Marne-la-Vallée, Fance

We construct explicit polynomial realizations of some combinatorial Hopf algebras based on various kinds of trees or forests, and some more general classes of graphs, ranging from the Connes–Kreimer algebra to an algebra of labelled forests isomorphic to the Hopf algebra of parking functions and to a new noncommutative algebra based on endofunctions admitting many interesting subalgebras and quotients.

Keywords: Hopf algebras of decorated rooted trees, free quasi-symmetric functions, parking functions

Foissy Loïc, Novelli Jean-Christophe, Thibon Jean-Yves: Polynomial realizations of some combinatorial Hopf algebras. J. Noncommut. Geom. 8 (2014), 141-162. doi: 10.4171/JNCG/151