Five interpretations of Faà di Bruno's formula
arXiv:1402.5551
Abstract
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.
Dyson-Schwinger Equations and Faà di Bruno Hopf Algebras in Physics and Combinatorics, Strasbourg : France (2011)