Article

A sufficient condition for a quandle to be latin

Journal of Combinatorial Designs

António Lages; Petr Vojtěchovský; Pedro Lopes — 2022

Key information

Authors:

António Lages (António José Marcos Lages); Petr Vojtěchovský; Pedro Lopes (Pedro Miguel Marques Francisco Lopes)

Published in

January 11, 2022

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.

Publication details

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Title of the publication container

Journal of Combinatorial Designs

First page or article number

251

Last page

259

Volume

30

Issue

04

Fields of Science and Technology (FOS)

mathematics - Mathematics

Publication language (ISO code)

eng - English

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