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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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) Vol. 254; pp. 79 - 117
Main Authors: Gálvez-Carrillo, Imma, Kock, Joachim, Tonks, Andrew
Format: Journal Article Publication
Language:English
Published: Elsevier Inc 20.03.2014
Subjects:
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 Access:Get full text
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Description
Summary: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