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Inversion of integral series enumerating planar trees

Jean-Louis Loday
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Abstract

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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Jean-Louis Loday. 2004-09-10. Inversion of integral series enumerating planar trees. https://arxiv.org/abs/math/0403316

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