Representations and identities of plactic-like monoids
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 analysi...
| Main Authors: | , , , |
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| Format: | Article in Journal/Newspaper |
| Language: | unknown |
| Published: |
arXiv
2021
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| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.2107.04492 https://arxiv.org/abs/2107.04492 |
| Summary: | 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 $2$. : 31 pages |
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