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arXiv · 2604.13989

Computing least common multiples in monoids with a finite Garside family

Emir Melliti
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Abstract

Right-reversing is an algorithm used to compute least common multiples in monoids that admit a right-complemented presentation. The algorithm can either terminate and find a result, fail, or run indefinitely. The correctness of the algorithm can be proved with additional assumptions coming from Garside theory. In the same framework, we prove that a non-terminating run of the algorithm is necessarily cyclic. Stopping when a cycle is detected provides a way of computing a minimal Garside family.

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Emir Melliti. 2026-04-15. Computing least common multiples in monoids with a finite Garside family. https://arxiv.org/abs/2604.13989

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