3 problems

Universality conjecture. For every pair of distinct odd primes $(p,q)$, the set $\mathcal{D}^*$ is the unique maximiser of $E(p^2q^3,\mathcal{D})$ over all admissible $\mathcal{D}$…

Let $n$ be a positive integer, and let $S_{1},S_{2}$ be symmetric subsets of $\mathbb{Z}_{n}$ without the identity such that $\operatorname{Cay}(\mathbb{Z}_{n},S_{1})$ and…

Framing conjecture. Suppose that all $\Lambda^0(d),\ldots,\Lambda^j(d)$ exist and that $\Lambda^j(d)$ is unframed. Then $\Lambda^0(d),\ldots,\Lambda^{j-1}(d)$ are all framed.