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arXiv · 2204.03523

The Word Problem is Solvable for 3-free Artin groups in Quadratic Time

Rubén Blasco-García·María Cumplido·Rose Morris-Wright
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Abstract

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, given two geodesic words representing the same element, one can obtain one from the other by using a set of homogeneous relations that never increase the word length.

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Rubén Blasco-García, María Cumplido, Rose Morris-Wright. 2022-04-07. The Word Problem is Solvable for 3-free Artin groups in Quadratic Time. https://arxiv.org/abs/2204.03523

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