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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 consequence is a proof of a conjecture of Kubat and Okniński that every plactic monoid of finite rank satisfies a non-trivial …
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The quantum plactic algebra is defined to be... | Find, read and cite all the research you need on ResearchGate. Conference Paper. Quantum Plactic and Pseudo-Plactic Algebras. December 2016;
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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 …
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Title: Plactic monoids satisfy nontrivial identities. Authors: Jan Okniński. Download PDF Abstract: It is shown that the plactic monoid P_n of any fixed rank n satisfies a nontrivial identity. Subjects: Group Theory (math.GR) MSC classes: 20M05, 20M07, 05E10: Cite as: arXiv:1902.06251 [math.GR]
the plactic monoid, to facilitate discussion of how the plactic monoid elements and multiplication are used in plactic signatures. Elements of the plactic monoid are semistandard tableaus. Elements of the plactic monoid can also be represented by sequences. The canonical sequence representation is the row reading, a concatenation of the tableau ...
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