4 problems

Let $G$ be a finite cyclic group, and let $S,T\subseteq G$ be a primitive formally dual pair, meaning a formally dual pair that is not obtained from a formally dual pair in a prope…

Let ${\mathbb{Z}}_N$ be the cyclic group of $N$ elements. A subset $T\subseteq {\mathbb{Z}}_N$ is primitive if it is not contained in any proper coset of ${\mathbb{Z}}_N$, and a su…

Cohn's conjecture. The subsets $\{0\}\subset \mathbb{Z}/\mathbb{Z}$ and $\operatorname{TITO}\subset \mathbb{Z}/4\mathbb{Z}$ are the only primitive formal-dual subsets of cyclic gro…

Let $G$ be a cyclic finite abelian group. A pair of subsets $S\subseteq G$ and $T\subseteq \widehat{G}$ is a primitive formally dual configuration if $S$ is not contained in a cose…