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Rewriting in Artin groups without A₃ or B₃ subdiagrams

Lookup NU author(s): Professor Sarah Rees

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Abstract

© 2026 The Author(s)We prove that the word problem in an Artin group G based on a diagram without A3 or B3 subdiagrams can be solved using a system of length preserving rewrite rules which, together with free reduction, can be used to reduce any word over the standard generators of G to a geodesic word in G in quadratic time. This result builds on work of Holt and Rees, and of Blasco-García, Cumplido and Morris-Wright. Those articles prove the same result for all Artin groups that are either sufficiently large or 3-free, respectively.

Publication metadata

Author(s): Blasco-Garcia R, Cumplido M, Holt DF, Morris-Wright R, Rees S

Publication type: Article

Publication status: Published

Journal: Journal of Algebra

Year: 2026

Volume: 703

Pages: 374-421

Print publication date: 01/10/2026

Online publication date: 05/03/2026

Acceptance date: 02/04/2018

Date deposited: 10/07/2026

ISSN (print): 0021-8693

ISSN (electronic): 1090-266X

Publisher: Academic Press Inc.

URL: https://doi.org/10.1016/j.jalgebra.2026.02.017

DOI: 10.1016/j.jalgebra.2026.02.017

Data Access Statement: No data was used for the research described in the article.

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