Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees

Gálvez-Carrillo, Imma, Kock, Joachim and Tonks, Andrew (2014) Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees. Advances in Mathematics, 254. pp. 79-117. ISSN 1090-2082

Abstract

We prove a Faa di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids.

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