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 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article Publikace |
| Jazyk: | angličtina |
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Elsevier Inc
20.03.2014
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| ISSN: | 0001-8708, 1090-2082 |
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| Abstract | 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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| AbstractList | 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.
Peer Reviewed 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. |
| Author | Tonks, Andrew Gálvez-Carrillo, Imma Kock, Joachim |
| Author_xml | – sequence: 1 givenname: Imma surname: Gálvez-Carrillo fullname: Gálvez-Carrillo, Imma email: m.immaculada.galvez@upc.edu organization: Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Escola dʼEnginyeria de Terrassa, Carrer Colom 1, 08222 Terrassa (Barcelona), Spain – sequence: 2 givenname: Joachim surname: Kock fullname: Kock, Joachim email: kock@mat.uab.cat organization: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain – sequence: 3 givenname: Andrew surname: Tonks fullname: Tonks, Andrew email: a.tonks@londonmet.ac.uk organization: STORM, London Metropolitan University, 166-220 Holloway Road, London N7 8DB, UK |
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| Keywords | Trees Polynomial functors Groupoids Homotopy cardinality Bialgebras Perturbative methods of renormalisation |
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| Snippet | 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... |
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| SubjectTerms | 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 |
| Title | Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees |
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