A Sufficient Condition for a Quandle to be Latin
Combinatorics
2021-12-10 v3
Abstract
A quandle is an algebraic structure satisfying three axioms: idempotency, right-invertibility and right self-distributivity. In quandles, right translations are permutations. The profile of a quandle is the list of cycle structures, one per right translation in the quandle. In this note we prove that if, for each cycle structure in the profile of a quandle, no two cycle lengths are equal, then the quandle is latin -- this is the sufficient condition mentioned in the title.
Cite
@article{arxiv.2104.10199,
title = {A Sufficient Condition for a Quandle to be Latin},
author = {António Lages and Pedro Lopes and Petr Vojtěchovský},
journal= {arXiv preprint arXiv:2104.10199},
year = {2021}
}
Comments
8 pages