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تسجيل مستخدم جديدRepresentations and identities of plactic-like monoids
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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 $mathcal{H}$ (respectively, $mathcal{F}$) forming a proper subvariety of the variety generated by the plactic monoid of rank $2$.
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We exhibit a faithful representation of the plactic monoid of every finite rank as a monoid of upper triangular matrices over the tropical semiring. This answers a question first posed by Izhakian and subsequently studied by several authors. A conseq
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