Garside families in Artin-Tits monoids and low elements in Coxeter groups.

DOI10.1016/j.crma.2015.01.008zbMath1329.20068arXiv1411.7498OpenAlexW2019523647MaRDI QIDQ2346879

Christophe Hohlweg, Patrick Dehornoy, Matthew J. Dyer

Publication date: 5 June 2015

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.7498

zbMATH Keywords

Coxeter groupslow elementsfinite Garside familiesfinitely generated Artin-Tits groupsright weak order

Mathematics Subject Classification ID

Free semigroups, generators and relations, word problems (20M05) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (10)

Automata, reduced words and Garside shadows in Coxeter groups. ⋮ Garside and Quadratic Normalisation: A Survey ⋮ Small roots, low elements, and the weak order in Coxeter groups ⋮ \(n\)-low elements and maximal rank \(k\) reflection subgroups of Coxeter groups ⋮ Left regular representations of Garside categories I. C^*-algebras and groupoids ⋮ Coherent presentations of monoids with a right-Noetherian Garside family ⋮ Discrete Morse theory and a reformulation of theK(π,1)-conjecture ⋮ Asymptotic combinatorics of Artin-Tits monoids and of some other monoids ⋮ Coxeter systems for which the Brink-Howlett automaton is minimal ⋮ Cone types, automata, and regular partitions in Coxeter groups

Cites Work

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• Reflection subgroups of Coxeter systems
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• A note on words in braid monoids
• A finiteness property and an automatic structure for Coxeter groups
• Bruhat intervals, polyhedral cones and Kazhdan-Lusztig-Stanley polynomials
• Foundations of Garside theory
• Artin-Gruppen und Coxeter-Gruppen
• Combinatorics of Coxeter Groups
• Groupes de Garside
• Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
• Basic Questions on Artin-Tits groups
• Asymptotical Behaviour of Roots of Infinite Coxeter Groups

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