Remark on the identities of the grammic monoid with three generators

DOI10.1007/S00233-022-10323-0arXiv2210.06017MaRDI QIDQ6413670

M. V. Volkov

Publication date: 12 October 2022

Abstract: Grammic monoids have recently been introduced by Christian Choffrut in terms of the action of the free monoid over a fixed ordered alphabet $X$ on the set of rows of Young tableaux filled with elements from $X$ via Schensted's insertion. For $X=a,b,c$ with $a<b<c$, Choffrut has identified the grammic monoid on $X$ with the quotient of the plactic monoid on $X$ over the congruence generated by the pair $(bacb,cbab)$. Since $cbabebcab$ in the latter monoid, the quotient is proper. We show that, nevertheless, the plactic and the grammic monoids with three generators satisfy the same identities.

Mathematics Subject Classification ID

General structure theory for semigroups (20M10) Free semigroups, generators and relations, word problems (20M05)

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