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 $k\geq 2$. In this article we provide a counterexample against this conjecture.