Fa\`a di Bruno Hopf algebras
Combinatorics
2022-01-17 v3 High Energy Physics - Theory
Abstract
This is a short review on the Fa\`a di Bruno formulas, and some Hopf algebras associated to them. These allow, among several other things, a short proof of the Lie-Scheffers theorem, and relating the Lagrange inversion formulas with antipodes. The link of Fa\`a di Bruno formulas with the theory of set partitions is developed in some detail.
Keywords
Cite
@article{arxiv.math/0508337,
title = {Fa\`a di Bruno Hopf algebras},
author = {Héctor Figueroa and José M. Gracia-Bondía and Joseph C. Várilly},
journal= {arXiv preprint arXiv:math/0508337},
year = {2022}
}
Comments
Latex, 9 pages. Originally commissioned as an encyclopedia article. v2: Updated with 9 new references. v3: Abstract added, misprints corrected. To appear in Revista Colombiana de Matem\'atica