Inversion of integral series enumerating planar trees

Details Inversion of integral series enumerating planar trees Inversion of integral series enumerating planar trees

2004-03-19

arxiv.org/abs/math/0403316v2

S\'em. Lothar. Combin. 53 (2004/05), Art. B53d, 16 pp.

Mathematics

Combinatorics

Minor modifications and reference to further work

Scientific paper

We consider an integral series f(X,t) which depends on the choice of a set X
of labelled planar rooted trees. We prove that its inverse for composition is
of the form f(Z,t) for another set Z of trees, deduced from X. The proof is
self-contained, though inspired by the Koszul duality theory of quadratic
operads.

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