Trees, functional equations, and combinatorial Hopf algebras

Details Trees, functional equations, and combinatorial Hopf algebras Trees, functional equations, and combinatorial Hopf algebras

2007-01-19

arxiv.org/abs/math/0701539v1

Mathematics

Combinatorics

14 pages, LaTEX

Scientific paper

One of the main virtues of trees is to represent 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.

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