Representations and identities of plactic-like monoids

Cain, Alan J.; Johnson, Marianne; Kambites, Mark; Malheiro, António

http://hdl.handle.net/10362/145310

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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 H (respectively, F) and forms a proper subvariety of the variety generated by the plactic monoid of rank 2.

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Baxter monoid Hypoplactic monoid Plactic monoid Representation Semigroup identity Stalactic monoid Sylvester monoid Taiga monoid Tropical semiring Upper triangular matrix semigroup Varieties Algebra and Number Theory