On the first order theory of plactic monoids

Combinatorial aspects of representation theory (05E10) Algebraic theory of languages and automata (68Q70) Semigroups in automata theory, linguistics, etc. (20M35) Quantifier elimination, model completeness, and related topics (03C10)

Cites Work

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Plactic algebra of rank 3
Finite Gröbner-Shirshov bases for plactic algebras and biautomatic structures for plactic monoids.
A plactic algebra for semisimple Lie algebras
On crystal bases of the \(q\)-analogue of universal enveloping algebras
Combinatoire et représentation du groupe symétrique. Actes de la Table Ronde du C.N.R.S. tenue à l'Université Louis-Pasteur de Strasbourg, 26 au 30 avril 1976
Schensted-type correspondence, plactic monoid, and jeu de taquin for type \(C_n\)
Irreducible affine varieties over a free group. I: Irreducibility of quadratic equations and Nullstellensatz
Schensted-type correspondences and plactic monoids for types \(B_n\) and \(D_n\)
Crystal monoids \& crystal bases: rewriting systems and biautomatic structures for plactic monoids of types \(A_{n}\), \(B_{n}\), \(C_{n}\), \(D_{n}\), and \(G_{2}\)
Identities in upper triangular tropical matrix semigroups and the bicyclic monoid
Diophantine geometry over groups. I: Makanin-Razborov diagrams
On the hypoplactic monoid
Definable groups in models of Presburger arithmetic
On equations and first-order theory of one-relator monoids
Representations and identities of plactic-like monoids
The stylic monoid
Plactic monoids: a braided approach
Identities of the plactic monoid.
Combinatorics of crystal graphs and Kostka-Foulkes polynomials for the root systems \(B_{n}\), \(C_{n}\) and \(D_{n}\)
Permutations, matrices, and generalized Young tableaux
Deciding conjugacy in sylvester monoids and other homogeneous monoids
EQUATIONS IN A FREE GROUP
Longest Increasing and Decreasing Subsequences
Tropical representations and identities of plactic monoids
WORD EQUATIONS OVER GRAPH PRODUCTS
ON SYSTEMS OF EQUATIONS IN A FREE GROUP
On the completeness of a certain system of arithmetic of whole numbers in which addition occurs as the only operation
THE PROBLEM OF SOLVABILITY OF EQUATIONS IN A FREE SEMIGROUP
Tarski’s problem about the elementary theory of free groups has a positive solution
Model Theory
Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids
Concatenation as a basis for arithmetic
Group equations with abelian predicates

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