Abstract
We give two explicit (quadratic) presentations of the plactic monoid in row and column generators correspondingly. Then we give direct independent proofs that these presentations are Gröbner–Shirshov bases of the plactic algebra in deg-lex orderings of generators. From Composition-Diamond lemma for associative algebras it follows that the set of Young tableaux is the Knuth normal form for plactic monoid ([30], see also Ch. 5 in [32]).
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