Rewriting in Artin groups without A_3 or B_$ subdiagrams
Rub'en Blasco-Garc'ia, Mar'ia Cumplido, Derek F. Holt,
Rose Morris-Wright and Sarah Rees
Keywords
Artin groups, word problem
Status
Submitted for publication
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, 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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