A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn's formula
arXiv:2003.01574 · doi:10.1016/j.ejc.2021.103406
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.
25 pages