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

Published 3 Mar 2020 in math.RA, math.CO, math.PR, and math.RT | (2003.01574v4)

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.

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