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Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees |
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| Authors: | Imma Gálvez-Carrillo Joachim Kock Andrew Tonks |
| Institution: | 1. Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Escola d?Enginyeria de Terrassa, Carrer Colom 1, 08222 Terrassa (Barcelona), Spain;2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain;3. STORM, London Metropolitan University, 166-220 Holloway Road, London N7 8DB, UK |
| 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. |
| Keywords: | Trees Groupoids Homotopy cardinality Polynomial functors Bialgebras Perturbative methods of renormalisation |
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