Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees
Imma Galvez-Carrillo, Joachim Kock, Andrew Tonks
TL;DR
This paper establishes a Faa di Bruno formula for Green functions within the bialgebra of P-trees, utilizing groupoid equivalences and homotopy cardinality to extend combinatorial and algebraic understanding.
Contribution
It introduces a novel Faa di Bruno formula for Green functions in P-tree bialgebras, connecting groupoid theory with algebraic combinatorics.
Findings
Faa di Bruno formula derived for Green functions in P-tree bialgebras
Use of groupoid equivalences and homotopy cardinality in the proof
Extension of combinatorial algebraic techniques to polynomial endofunctors
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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