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math.GR2025
The Word Problem is Solvable for 3-free Artin groups in Quadratic Time
Rubén Blasco-GarcÃa, MarÃa Cumplido, Rose Morris-Wright
We give a quadratic-time explicit and computable algorithm to solve the word problem for Artin groups that do not contain any relations of length 3. Furthermore, we prove that, giv…
math.GR2024
Rewriting in Artin groups without A_3 or B_3 subdiagrams
Rubén Blasco-GarcÃa, MarÃa Cumplido, Derek F. Holt +2
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…
math.GR2024
Acylindrical hyperbolicity for Artin groups with a visual splitting
Ruth Charney, Alexandre Martin, Rose Morris-Wright
We establish a criterion that implies the acylindrical hyperbolicity of many Artin groups admitting a visual splitting. This gives a variety of new examples of acylindrically hyper…