Polynomial realizations of some combinatorial Hopf algebras
Combinatorics
2011-09-22 v2
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.
Keywords
Cite
@article{arxiv.1009.2067,
title = {Polynomial realizations of some combinatorial Hopf algebras},
author = {L. Foissy and J. -C. Novelli and J. -Y. Thibon},
journal= {arXiv preprint arXiv:1009.2067},
year = {2011}
}
Comments
20 pages