R-equivalence classes of $\mathrm{Rot}{\mathbb{E}}^2$-colorings of torus knots

Abstract

We introduce a new equivalence relation, named R-equivalence relation, on the set of colorings of an oriented knot diagram by a quandle. We determine the R-equivalence classes of colorings of a diagram of a torus knot by a quandle, called $\mathrm{Rot}{\mathbb{E}}^2$, under a certain condition.

28 pages, 13 figures