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.
Cite this article
Loïc Foissy, Jean-Christophe Novelli, Jean-Yves Thibon, Polynomial realizations of some combinatorial Hopf algebras. J. Noncommut. Geom. 8 (2014), no. 1, pp. 141–162DOI 10.4171/JNCG/151