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arXiv · 1106.4753

New approaches to plactic monoid via Gröbner-Shirshov bases

L. A. Bokut·Yuqun Chen·Weiping Chen·Jing Li
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Abstract

We present the plactic algebra on an arbitrary alphabet set $A$ by row generators and column generators respectively. We give Gröbner-Shirshov bases for such presentations. In the case of column generators, a finite Gröbner-Shirshov basis is given if $A$ is finite. From the Composition-Diamond lemma for associative algebras, it follows that the set of Young tableaux is a linear basis of plactic algebra. As the result, it gives a new proof that Young tableaux are normal forms of elements of plactic monoid. This result was proved by D.E. Knuth \cite{Knuth} in 1970, see also Chapter 5 in \cite{M.L}.

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L. A. Bokut, Yuqun Chen, Weiping Chen, Jing Li. 2014-10-03. New approaches to plactic monoid via Gröbner-Shirshov bases. https://arxiv.org/abs/1106.4753

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