Trees, functional equations, and combinatorial Hopf algebras

Authors:
Florent Hivert;Jean-Christophe Novelli;Jean-Yves Thibon
Affiliations:
LITIS, Université de Rouen, Avenue de l'université, 76801 Saint ítienne du Rouvray, France;Institut Gaspard Monge, Université de Marne-la-Vallée, 5, Boulevard Descartes Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France;Institut Gaspard Monge, Université de Marne-la-Vallée, 5, Boulevard Descartes Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France
Venue:
European Journal of Combinatorics
Year:
2008

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Abstract

One of the main virtues of trees is the representation of formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in power series rings. When analyzed in terms of combinatorial Hopf algebras, the simplest examples yield interesting algebraic identities or enumerative results.