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Trees, functional equations, and combinatorial Hopf algebras. (English) Zbl 1227.05272
Summary: 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.

05E15 Combinatorial aspects of groups and algebras (MSC2010)
05C05 Trees
16T05 Hopf algebras and their applications
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