Representations and identities of plactic-like monoids

Publisher Copyright: © 2022 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 ch...

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Bibliographic Details
Published in:Journal of Algebra
Main Authors: Cain, Alan J., Johnson, Marianne, Kambites, Mark, Malheiro, António
Other Authors: CMA - Centro de Matemática e Aplicações, DM - Departamento de Matemática
Format: Article in Journal/Newspaper
Language:English
Published: 2022
Subjects:
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
Baxter
Patience
taiga
Online Access:http://hdl.handle.net/10362/145310
https://doi.org/10.1016/j.jalgebra.2022.04.033
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Summary:Publisher Copyright: © 2022 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. publishersversion published

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