On Maximal $S$-Free Sets and the Helly Number for the Family of $S$-Convex Sets
On Maximal $S$-Free Sets and the Helly Number for the Family of $S$-Convex Sets
We study two combinatorial parameters, which we denote by $f(S)$ and $h(S)$, associated with an arbitrary set $S \subseteq \mathbb{R}^d$, where $d \in \mathbb{N}$. In the nondegenerate situation, $f(S)$ is the largest possible number of facets of a $d$-dimensional polyhedron $L$ such that the interior of $L$ is disjoint with …