The Lexicographic Cross-Section of the Plactic Monoid Is Regular
نویسندگان
چکیده
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 characterization of these minimal elements and show that constructing them is as fast as constructing a tableau.
منابع مشابه
Radix Cross-Sections for Length Morphisms
We prove that the radix cross-section of a rational set for a length morphism, and more generally for a rational function from a free monoid into N, is rational, a property that does not hold any more if the image of the function is a subset of a free monoid with two or more generators. proceedings short version1 The purpose of this paper is to give a positive answer to a problem left open in a...
متن کاملThe 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...
متن کاملFinite convergent presentation of plactic monoid for type C
We give an explicit presentation for the plactic monoid for type C using admissible column generators. Thanks to the combinatorial properties of symplectic tableaux, we prove that this presentation is finite and convergent. We obtain as a corollary that plactic monoids for type C satisfy homological finiteness properties.
متن کاملThe 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...
متن کاملSchensted-Type correspondence, Plactic Monoid and Jeu de Taquin for type Cn
We use Kashiwara’s theory of crystal bases to study the plactic monoid for Uq(sp2n). Then we describe the corresponding insertion and sliding algorithms. The sliding algorithm is essentially the symplectic Jeu de Taquin defined by Sheats and our construction gives the proof of its compatibility with plactic relations.
متن کامل