The affine type C difference-set conjecture

Let $V_C=\left(\mathbb{Z}/(2n+1)\mathbb{Z}\right)^n$ and let $\mathcal{C}_n$ be the subset defined in the paper from the affine type C residue conditions. Affine type C difference-set conjecture. For any integer $n\geq1$,

$$\mathcal{C}_n-\mathcal{C}_n=V_C=\left(\mathbb{Z}/(2n+1)\mathbb{Z}\right)^n.$$

This sumset equality would imply universality of the entropy on the affine Weyl group of type C; it is supported by computational experiments and remains open in general.