Representations and identities of plactic-like monoids

A. J. Cain, M. Johnson, Kambites Malheiro M. A. "Representations and identities of plactic-like monoids." Journal of Algebra. 606 (2022): 819-850.


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 analysing the image of these representations, we show that the variety generated by a single hypoplactic (respectively, stalactic or taiga) monoid of rank at least 2 coincides with the variety generated by the natural numbers together with a fixed finite monoid (respectively, F) and forms a proper subvariety of the variety generated by the plactic monoid of rank 2.

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