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Representations and identities of plactic-like monoids
Authors
Alan J. Cain
Marianne Johnson
Mark Kambites
António Malheiro
Publication date
15 September 2022
Publisher
'Elsevier BV'
Doi
Cite
Abstract
Funding Information: The first and fourth authors were supported by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Centre for Mathematics and Applications) and PTDC/MAT-PUR/31174/2017. Publisher Copyright: © 2022We 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.publishersversionpublishe
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Last time updated on 15/11/2022