New approach to Schensted-Knuth normal forms

Details New approach to Schensted-Knuth normal forms New approach to Schensted-Knuth normal forms

2011-06-23

arxiv.org/abs/1106.4753v1

Mathematics

Rings and Algebras

14 pages

Scientific paper

We present the plactic algebra on an arbitrary alphabet set $A$ by row generators and we give a Gr\"{o}bner-Shirshov basis for such a presentation. 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 in 1970.

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