3 problems

Magic-relation conjecture. A sector produces a magic relation if and only if its critical variety has a higher-dimensional component.

Let $f\in\mathcal{B}(k,n)$ be loopless and assume that the crossing graph $G_f^\times$ is connected. Let $\Theta_f^\circ$ be the admissible parameter space, let…

Let $f\in\mathcal{B}(k,n)$ be loopless. Let $G_f^\times$ be the graph on $[n]$ whose edges are the pairs forming an $f$-crossing, let $\operatorname{conn}_f$ be its number of conne…