Cone types, automata, and regular partitions in Coxeter groups

DOI10.1016/j.aim.2021.108146OpenAlexW4220674055MaRDI QIDQ2078851

Yanyan Li

Publication date: 4 March 2022

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.09962

zbMATH Keywords

Coxeter groupsautomataroot systemsGarside shadowslow elements

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Root systems (17B22)

Uses Software

• Magma

Cites Work

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• Automata, reduced words and Garside shadows in Coxeter groups.
• Small roots, low elements, and the weak order in Coxeter groups
• A finiteness property and an automatic structure for Coxeter groups
• The Magma algebra system. I: The user language
• Coxeter systems for which the Brink-Howlett automaton is minimal
• The dominance hierarchy in root systems of Coxeter groups.
• Garside families in Artin-Tits monoids and low elements in Coxeter groups.
• Combinatorics of Coxeter Groups
• Buildings
• On the root system of a coxeter group
• On the Weak Order of Coxeter Groups
• Alcoves Corresponding to an Affine Weyl Group
• Sign Types Corresponding to an Affine Weyl Group

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