5 citations · 18 across the 20 of their papers we have counts for
28 papers
Constructing an infinite family of quandles from a quandle
Pedro Lopes, Manpreet Singh
Quandles are self-distributive, right-invertible, idempotent algebras. A group with conjugation for binary operation is an example of a quandle. Given a quandle and a p…
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…
On the orbits associated with the Collatz conjecture
Louis Kauffman, Pedro Lopes
This article is based upon previous work by Sousa Ramos and his collaborators. They first prove that the existence of only one orbit associated with the Collatz conjecture is equiv…
The Prevalence of Persistent Tangles
Louis H. Kauffman, Pedro Lopes
This article addresses persistent tangles. These are tangles whose presence in a knot diagram forces that diagram to be knotted. We provide new methods for constructing persistent…
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…