<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">A. J. Cain, M. Johnson, M. Kambites, A. Malheiro</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Representations and identities of plactic-like monoids</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Algebra</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1016/j.jalgebra.2022.04.033</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">606</style></volume><pages><style face="normal" font="default" size="100%">819--850</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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.&lt;/p&gt;
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