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A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn’s formula
European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2021-08-19 , DOI: 10.1016/j.ejc.2021.103406 Laura Colmenarejo 1 , Joscha Diehl 2 , Miruna-Ştefana Sorea 3, 4
中文翻译:
洗牌代数中的二次恒等式和 de Bruijn 公式的另一种证明
更新日期:2021-08-19
European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2021-08-19 , DOI: 10.1016/j.ejc.2021.103406 Laura Colmenarejo 1 , Joscha Diehl 2 , Miruna-Ştefana Sorea 3, 4
Affiliation
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.
中文翻译:
洗牌代数中的二次恒等式和 de Bruijn 公式的另一种证明
由某些迭代积分的多项式恒等式激发,首先在 Colmenarejo 等人中观察到。(2020)在格路径的设置中,我们证明了混洗代数中一个有趣的组合恒等式。当在路径签名的框架中解释时,它与de Bruijn 的公式密切相关。