A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn's formula. (January 2022)

• Record Type: Journal Article
• Authors: Colmenarejo, Laura; Diehl, Joscha; Sorea, Miruna-Ştefana
• Is Part Of: European journal of combinatorics. Volume 99(2022)
• Publication Date: 2022-01
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2021.103406
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: Motivated by a polynomial identity of certain iterated integrals, first observed in Colmenarejo et al. (2020) 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.