Séminaire Lotharingien de Combinatoire, B49c (2003), 45 pp.

Abdelmalek Abdesselam

Feynman Diagrams in Algebraic Combinatorics

Abstract. 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, an easy access to the wonderland of quantum field theory.

Received: December 9, 2002. Revised: August 17, 2003. Accepted: November 4, 2003.

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