Computing least common multiples in monoids with a finite Garside family
Group Theory
2026-04-16 v1
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.
Keywords
Cite
@article{arxiv.2604.13989,
title = {Computing least common multiples in monoids with a finite Garside family},
author = {Emir Melliti},
journal= {arXiv preprint arXiv:2604.13989},
year = {2026}
}
Comments
30 pages, 16 figures, associated code available at https://github.com/domyrmininon/compute_gf