Finite Grobner-Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids

摘要

This paper shows that every Plactic algebra of finite rank admits a finite Grobner-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 FP infinity. Also, answering a question of Zelmanov, we apply this rewriting system and other techniques to show that Plactic monoids of finite rank are biautomatic. (C) 2014 Elsevier Inc. All rights reserved.