Five interpretations of Faà di Bruno's formula

Alessandra Frabetti (1) , Dominique Manchon (2)

1 ICJ - Institut Camille Jordan
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

In these lectures we present five interpretations of the Fa' di Bruno formula which computes the n-th derivative of the composition of two functions of one variable: in terms of groups, Lie algebras and Hopf algebras, in combinatorics and within operads.

Keywords: Proalgebraic groups; Hopf algebras; Operads

Domains: Combinatorics [math.CO]; Commutative Algebra [math.AC]; Group Theory [math.GR]; Quantum Algebra [math.QA]; Mathematical Physics [math-ph]

Alessandra Frabetti, Dominique Manchon. Five interpretations of Faà di Bruno's formula. Dyson-Schwinger Equations and Faà di Bruno Hopf Algebras in Physics and Combinatorics, Jun 2011, Strasbourg, France. pp.5-65. ⟨hal-00950525⟩