A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn's formula

3 Mar 2020 · Laura Colmenarejo, Joscha Diehl, Miruna-Stefana Sorea ·

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.