Counterexample to a conjecture about dihedral quandle

Abstract

It was conjectured that the augmentation ideal of a dihedral quandle of even order $n>2$ satisfies $|{\Delta }^k({\text{R}}_n)/{\Delta }^{k+1}({\text{R}}_n)|=n$ for all $k\ge 2$. In this article we provide a counterexample against this conjecture.

3 pages