Rewriting in Artin groups without A₃ or B₃ subdiagrams

2024/12/14 by Blasco-García, Rubén, Cumplido, María, Holt, Derek F. +2
#20F10 (Primary) 68R15 (Secondary) #20F36 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2412.12195

Abstract

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.

Related

• Artin groups of type (2,3,n)
• The Word Problem is Solvable for 3-free Artin groups in Quadratic Time
• Rewriting systems, plain groups, and geodetic graphs
• Rewriting systems in sufficiently large Artin-Tits groups
• Twisted right-angled Artin groups