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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Veröffentlicht in:	Advances in mathematics (New York. 1965) Jg. 254; S. 79 - 117
Hauptverfasser:	Gálvez-Carrillo, Imma, Kock, Joachim, Tonks, Andrew
Format:	Journal Article Verlag
Sprache:	Englisch
Veröffentlicht:	Elsevier Inc 20.03.2014
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 Trees Polynomial functors Groupoids Homotopy cardinality Bialgebras Perturbative methods of renormalisation
ISSN:	0001-8708, 1090-2082
Online-Zugang:	Volltext
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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