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

We prove a Faà 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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Vydáno v:	Advances in mathematics (New York. 1965) Ročník 254; s. 79 - 117
Hlavní autoři:	Gálvez-Carrillo, Imma, Kock, Joachim, Tonks, Andrew
Médium:	Journal Article Publikace
Jazyk:	angličtina
Vydáno:	Elsevier Inc 20.03.2014
Témata:	05 Combinatorics 05C Graph theory 20 Group theory and generalizations 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) 81 Quantum theory 81T Quantum field theory; related classical field theories Bialgebras Classificació AMS Física matemàtica Grafs, Teoria de Graph theory Group theory Groupoids Grupoides Grups, Teoria de Homotopy cardinality Matemàtiques i estadística Mathematical physics Perturbative methods of renormalisation Polynomial functors Teoria de categories; àlgebra homològica Teoria de grups Trees Àlgebra Àrees temàtiques de la UPC Trees Polynomial functors Groupoids Homotopy cardinality Bialgebras Perturbative methods of renormalisation
ISSN:	0001-8708, 1090-2082
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Popis
Shrnutí:	We prove a Faà 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.
ISSN:	0001-8708 1090-2082
DOI:	10.1016/j.aim.2013.12.015