<?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%">Cain, A.J.</style></author><author><style face="normal" font="default" size="100%">R.D. {Gray}</style></author><author><style face="normal" font="default" size="100%">Malheiro, A.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Finite Gröbner-Shirshov bases for plactic algebras and biautomatic structures for plactic monoids.</style></title><secondary-title><style face="normal" font="default" size="100%">J. Algebra</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://dx.doi.org/10.1016/j.jalgebra.2014.09.037</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Elsevier (Academic Press), San Diego, CA</style></publisher><volume><style face="normal" font="default" size="100%">423</style></volume><pages><style face="normal" font="default" size="100%">37–53</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper shows that every Plactic algebra of finite rank admits a finite Gröbner--Shirshov basis. The result is proved by using the combinatorial properties of Young tableaux to construct a finite complete rewriting system for the corresponding Plactic monoid, which also yields the corollaries that Plactic monoids of finite rank have finite derivation type and satisfy the homological finiteness properties left and right $\mathrm{FP}_\infty$. Also, answering a question of Zelmanov, we apply this rewriting system and other techniques to show that Plactic monoids of finite rank are biautomatic.&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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