New approaches to plactic monoid via Gröbner-Shirshov bases.

DOI10.1016/j.jalgebra.2014.10.010zbMath1309.16014arXiv1106.4753OpenAlexW1993200013WikidataQ112881578 ScholiaQ112881578MaRDI QIDQ479745

Weiping Chen, Jing Li, Yuqun Chen, Leonid A. Bokut'

Publication date: 5 December 2014

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

Full work available at URL: https://arxiv.org/abs/1106.4753

zbMATH Keywords

Young tableauxsemigroup algebrasnormal form theoremsGröbner-Shirshov basesplactic 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) Semigroup rings, multiplicative semigroups of rings (20M25)

Related Items (9)

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 ⋮ Coherence for plactic monoids via rewriting theory and crystal structures ⋮ Plactic monoids: a braided approach ⋮ New approaches to plactic monoid via Gröbner-Shirshov bases. ⋮ Gröbner–Shirshov bases and their calculation

Cites Work

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• Lyndon-Shirshov basis and anti-commutative algebras
• Finite Gröbner-Shirshov bases for plactic algebras and biautomatic structures for plactic monoids.
• New approaches to plactic monoid via Gröbner-Shirshov bases.
• Gröbner-Shirshov bases for Rota-Baxter algebras.
• Gröbner-Shirshov bases for Lie algebras over a commutative algebra
• Selected works of A. I. Shirshov. Translated by Murray Bremner and Mikhail V. Kotchetov. Edited by Leonid A. Bokut, Victor Latyshev, Ivan Shestakov and Efim Zelmanov
• Composition-diamond lemma for tensor product of free algebras.
• The diamond lemma for ring theory
• Gröbner-Shirshov bases for irreducible \(sl_{n+1}\)-modules
• Gröbner-Shirshov bases for metabelian Lie algebras
• Gröbner-Shirshov bases: from their inception to the present time.
• Gröbner-Shirshov bases for semirings.
• Gröbner-Shirshov bases, conformal algebras, and pseudo-algebras.
• Permutations, matrices, and generalized Young tableaux
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Gröbner-Shirshov Bases for Plactic Algebras
• GRÖBNER–SHIRSHOV BASES AND EMBEDDINGS OF ALGEBRAS
• Longest Increasing and Decreasing Subsequences
• GRÖBNER–SHIRSHOV BASES FOR DIALGEBRAS
• GRÖBNER-SHIRSHOV BASES: SOME NEW RESULTS
• Standard Gröbner-Shirshov Bases of Free Algebras Over Rings, I
• Some Algorithmic Problems for Lie Algebras
• Some New Results on Gröbner-Shirshov Bases

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