A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn's formula
Rings and Algebras
2021-09-17 v4 Combinatorics
Probability
Representation Theory
Abstract
Motivated by a polynomial identity of certain iterated integrals, first observed in [CGM20] in the setting of lattice paths, we prove an intriguing combinatorial identity in the shuffle algebra. It has a close connection to de Bruijn's formula when interpreted in the framework of signatures of paths.
Cite
@article{arxiv.2003.01574,
title = {A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn's formula},
author = {Laura Colmenarejo and Joscha Diehl and Miruna-Stefana Sorea},
journal= {arXiv preprint arXiv:2003.01574},
year = {2021}
}
Comments
25 pages