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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Bibliographische Detailangaben
Veröffentlicht in:	Advances in mathematics (New York. 1965) 2014-03, Vol.254, p.79-117
Hauptverfasser:	Gálvez-Carrillo, Imma, Kock, Joachim, Tonks, Andrew
Format:	Artikel
Sprache:	eng
Schlagworte:	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
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Beschreibung
Zusammenfassung:	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