4 problems

Let $B=\{\mathbf{x}:\|\mathbf{x}\|_2\leq 1\}$ and $C=\{\mathbf{x}:g(\mathbf{x})\leq 0\}$, where $g$ is a quadratic polynomial. Suppose that $g$ has one of the forms … or … where…

Relaxation conjecture. In order to find a maximal $S$-free set, it should suffice to adequately relax the inequalities defining $C_{\phi_{\lambda}}$. The preceding example shows wh…

Two-convex-components conjecture. After analyzing low-dimensional instances, the complement

Binomial-ring generation conjecture. Every square-free solution of finite order can be "generated" from a binomial ring with skew polynomial relation.