<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>36</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Cain, A.J.</style></author><author><style face="normal" font="default" size="100%">Klein, G.</style></author><author><style face="normal" font="default" size="100%">Kubat, Ł.</style></author><author><style face="normal" font="default" size="100%">Malheiro, A.</style></author><author><style face="normal" font="default" size="100%">Okniński, J.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A note on identities in plactic monoids and monoids of upper-triangular tropical matrices</style></title><secondary-title><style face="normal" font="default" size="100%">ArXiv e-prints</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">05E99 (Primary)</style></keyword><keyword><style  face="normal" font="default" size="100%">14T05</style></keyword><keyword><style  face="normal" font="default" size="100%">16Y60 (Secondary)</style></keyword><keyword><style  face="normal" font="default" size="100%">20M30</style></keyword><keyword><style  face="normal" font="default" size="100%">Mathematics - Combinatorics</style></keyword><keyword><style  face="normal" font="default" size="100%">Mathematics - Group Theory</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/1705.04596</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt; This paper uses the combinatorics of Young tableaux to prove the plactic monoid of infinite rank does not satisfy a non-trivial identity, by showing that the plactic monoid of rank n cannot satisfy a non-trivial identity of length less than or equal to n. A new identity is then proven to hold for the monoid of n×n upper-triangular tropical matrices. Finally, a straightforward embedding is exhibited of the plactic monoid of rank 3 into the direct product of two copies of the monoid of 3×3 upper-triangular tropical matrices, giving a new proof that the plactic monoid of rank 3 satisfies a non-trivial identity. &lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;n/a&lt;/p&gt;
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