Polynomial realizations of some combinatorial Hopf algebras

Authors :: Foissy, L.
Novelli, J. -C.
Thibon, J. -Y.
Publication Year :: 2010
Abstract: We construct explicit polynomial realizations of some combinatorial Hopf algebras based on various kind 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.<br />Comment: 20 pages