Polynomial realizations of some combinatorial Hopf algebras

Details Polynomial realizations of some combinatorial Hopf algebras Polynomial realizations of some combinatorial Hopf algebras

2010-09-10

arxiv.org/abs/1009.2067v2

Mathematics

Combinatorics

20 pages

Scientific paper

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.

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