Identities of the plactic monoid

The Shifted Plactic Monoid

We introduce a shifted analog of the plactic monoid of Lascoux and Schützenberger, the shifted plactic monoid. It can be defined in two different ways: via the shifted Knuth relations, or using Haiman’s mixed insertion. Applications include: a new combinatorial derivation (and a new version of) the shifted Littlewood-Richardson Rule; similar results for the coefficients in the Schur expansion o...

The Plactic Monoid

The shifted plactic monoid ( extended abstract )

The (shifted) plactic monoid. The celebrated Robinson-Schensted-Knuth correspondence (14) is a bijection between words in a linearly ordered alphabet X = {1 < 2 < 3 < · · · } and pairs of Young tableaux with entries in X . More precisely, each word corresponds to a pair consisting of a semistandard insertion tableau and a standard recording tableau. The words producing a given insertion tableau...

The Lexicographic Cross-Section of the Plactic Monoid Is Regular

The plactic monoid is the quotient of the free monoid by the congruence generated by Knuth’s well-celebrated rules. It is well-known that the set of Young tableaux is a cross-section of this congruence which happens to be regular. The main result of this work shows that the set of alphabetically minimal elements in the congruence classes is also regular. We give a full combinatorial characteriz...

Recognizable Subsets of the Two Letter Plactic Monoid

The plactic monoid P la(a, b) on two letters will be studied from the point of view of classical language theory. In particular, we will give the fine structure of its recognizable subsets.