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Polynomial realizations of some combinatorial Hopf algebras (1009.2067v2)
Published 10 Sep 2010 in math.CO
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.
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