1207.6404 (Imma Galvez-Carrillo et al.)

Groupoids and Faa di Bruno formulae for Green functions in bialgebras of
trees    [PDF]

Imma Galvez-Carrillo, Joachim Kock, Andrew Tonks

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. For suitable choices of P, the result implies also formulae for Green functions in bialgebras of graphs.

View original: http://arxiv.org/abs/1207.6404