@article{5a1f4a8f2af64876938d584a2201bc7a,
title = "Groupoids and Fa{\`a} di Bruno formulae for Green functions in bialgebras of trees",
abstract = "We prove a Fa{\`a} 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, Bialgebras, Perturbative methods of renormalisation, Polynomial functors, Homotopy cardinality",
author = "Imma G{\'a}lvez-Carrillo and Andrew Tonks and Joachim Kock",
note = "Funding Information: The authors acknowledge the following MTM grants from the Spanish Government (MINECO) and SGR grants from the Generalitat de Catalunya . The first author was partially supported by grants MTM2010-15831 , MTM2010-20692 , SGR1092-2009 , and MTM2012-38122-C03-01 , the second author by MTM2009-10359 , MTM2010-20692 , and SGR1092-2009 , and the third author by MTM2010-15831 , SGR119-2009 . ",
year = "2014",
month = mar,
day = "20",
doi = "10.1016/j.aim.2013.12.015",
language = "English",
volume = "254",
pages = "79--117",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}