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arXiv · 2412.12195

Rewriting in Artin groups without A_3 or B_3 subdiagrams

Rubén Blasco-García·María Cumplido·Derek F. Holt·Rose Morris-Wright·Sarah Rees
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Abstract

We prove that the word problem in an Artin group G based on a diagram without A_3 or B_3 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-Garc\'ia, Cumplido and Morris-Wright. Those articles prove the same result for all Artin groups that are either sufficiently large or 3-free, respectively.

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Rubén Blasco-García, María Cumplido, Derek F. Holt, Rose Morris-Wright, Sarah Rees. 2024-12-14. Rewriting in Artin groups without A_3 or B_3 subdiagrams. https://arxiv.org/abs/2412.12195

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