English

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.

Keywords

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}
}

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25 pages