@article {15800,
	title = {Representations and identities of plactic-like monoids},
	journal = {Journal of Algebra},
	volume = {606},
	year = {2022},
	pages = {819--850},
	abstract = {<p>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  (respectively, F) and forms a proper subvariety of the variety generated by the plactic monoid of rank 2.</p>
},
	url = {https://doi.org/10.1016/j.jalgebra.2022.04.033},
	author = {A. J. Cain, M. Johnson, M. Kambites, A. Malheiro}
}
