Polynomial realizations of some combinatorial Hopf algebras

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.

20 pages

References in corpus (6)

• Hopf Algebras, Renormalization and Noncommutative Geometry
• Noncommutative symmetric functions
• Combinatorial Hopf algebras in quantum field theory I
• Polynomial realizations of some trialgebras
• Hopf-algebraic structures of families of trees
• Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras

Cited by in corpus (2)

• Hopf Algebras of m-permutations, (m+1)-ary trees, and m-parking functions
• Renormalization group-like proof of the universality of the Tutte polynomial for matroids