Quandles with one nontrivial column

Abstract

The axioms of a quandle imply that the columns of its Cayley table are permutations. This paper studies quandles with exactly one non-trivially permuted column. Their automorphism groups, quandle polynomials, (symmetric) cohomology groups, and $\mathrm{\text{Hom}}$ quandles are studied. The quiver and cocycle invariant of links using these quandles are shown to relate to linking number.