2011/06/23 by L. A. Bokut, Bokut, L. A., Yuqun Chen +4
Mathematics · #13P10 #16S15 #20M05 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1106.4753
openalex publication_date 2011/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citeKnuth in 1970, see also Chapter 5 in \citeM.L.