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Feynman diagrams in algebraic combinatorics. (English) Zbl 1034.81518

Summary: We show, in great detail, how the perturbative tools of quantum field theory allow one to rigorously obtain: a “categorified” Faà di Bruno type formula for multiple composition, an explicit formula for reversion and a proof of Lagrange-Good inversion, all in the setting of multivariable power series. We took great pains to offer a self-contained presentation that, we hope, will provide any mathematician who wishes easy access to the wonderland of quantum field theory.

MSC:

81T18 Feynman diagrams
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