Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees
arXiv:1207.6404 · doi:10.1016/j.aim.2013.12.015
Abstract
We prove a Faa 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.
v1: 48 pages, comments are welcome; v2: removed some material on graphs, expository improvements, 35 pages
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- A simplicial groupoid for plethysm
- Combinatorial Dyson-Schwinger equations and inductive data types
- Combinatorics and simplicial groupoids
- Antipodes of monoidal decomposition spaces