Representations and identities of plactic-like monoids

• Main Authors: Cain, Alan J., Johnson, Marianne, Kambites, Mark, Malheiro, António
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: arXiv 2021
• Subjects: Rings and Algebras math.RA; Combinatorics math.CO; Group Theory math.GR; FOS Mathematics; 20M07, 20M30, 05E99, 12K10, 16Y60; Baxter; Patience; taiga
• Online Access: https://dx.doi.org/10.48550/arxiv.2107.04492; https://arxiv.org/abs/2107.04492

We exhibit faithful representations of the hypoplactic, stalactic, taiga, sylvester, Baxter and right patience sorting monoids of each finite rank as monoids of upper triangular matrices over any semiring from a large class including the tropical semiring and fields of characteristic $0$. By analysi...