Polynomial realizations of some combinatorial Hopf algebras

摘要

We construct explicit polynomial realizations of some combinatorial Hopfalgebras based on various kind of trees or forests, and some more generalclasses of graphs, ranging from the Connes-Kreimer algebra to an algebra oflabelled forests isomorphic to the Hopf algebra of parking functions, and to anew noncommutative algebra based on endofunctions admitting many interestingsubalgebras and quotients.