5 papers
Super Hayashi Quandles
Antonio Lages, Pedro Lopes
Quandles are right-invertible, right-self distributive (and idempotent) algebraic structures. Therefore, right translations are quandle automorphisms. It has been interesting to lo…
On a Conjecture by Hayashi on Finite Connected Quandles
Antonio Lages, Pedro Lopes
A quandle is an algebraic structure whose binary operation is idempotent, right-invertible and right self-distributive. Right-invertibility ensures right translations are permutati…
A Proof of Euler's Theorem via Quandles
António Lages, Pedro Lopes
We prove Euler's theorem of number theory developing an argument based on quandles. A quandle is an algebraic structure whose axioms mimic the three Reidemeister moves of knot theo…
A Sufficient Condition for a Quandle to be Latin
António Lages, Pedro Lopes, Petr Vojtěchovský
A quandle is an algebraic structure satisfying three axioms: idempotency, right-invertibility and right self-distributivity. In quandles, right translations are permutations. The p…
Quandles of cyclic type with several fixed points
António Lages, Pedro Lopes
A quandle of cyclic type of order with fixed points is such that each of its permutations splits into cycles of length and one cycle of length . In this…