Finite Gröbner-Shirshov bases for plactic algebras and biautomatic structures for plactic monoids.

DOI10.1016/j.jalgebra.2014.09.037zbMath1311.20055arXiv1205.4885OpenAlexW2054644771MaRDI QIDQ479731

António Malheiro, Robert D. Gray, Alan J. Cain

Publication date: 5 December 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.4885

zbMATH Keywords

Young tableauxsemigroup algebrasGröbner-Shirshov basescomplete rewriting systemsbiautomatic monoidsplactic algebrasplactic monoids

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Free semigroups, generators and relations, word problems (20M05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Semigroups in automata theory, linguistics, etc. (20M35) Grammars and rewriting systems (68Q42) Semigroup rings, multiplicative semigroups of rings (20M25)

Related Items (19)

Automaticity of one-relator semigroups with length less than or equal to three ⋮ Crystal monoids \& crystal bases: rewriting systems and biautomatic structures for plactic monoids of types \(A_{n}\), \(B_{n}\), \(C_{n}\), \(D_{n}\), and \(G_{2}\) ⋮ Garside and Quadratic Normalisation: A Survey ⋮ The stylic monoid ⋮ Irreducible representations of the plactic algebra of rank four ⋮ Knuth's coherent presentations of plactic monoids of type A ⋮ Quivers of stylic algebras ⋮ Plactic key agreement (insecure?) ⋮ Plactic monoids: a braided approach ⋮ Tropical plactic algebra, the cloaktic monoid, and semigroup representations ⋮ The monoids of the patience sorting algorithm ⋮ New approaches to plactic monoid via Gröbner-Shirshov bases. ⋮ Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableaux ⋮ Gröbner–Shirshov bases and their calculation ⋮ On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids ⋮ Cohomology rings of the plactic monoid algebra via a Gröbner–Shirshov basis ⋮ Tropical representations and identities of plactic monoids ⋮ Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids ⋮ Identities of the plactic monoid.

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