Fixing and hindering systems in combinatorial geometry
Let \(F\) be a set in the boundary of a convex body \(M\subset \mathbb{R}^n\). The set \(F\) is a fixing system (a hindering system) for \(M\) if for every (oriented) direction here is a nontrivial translation \(t\) in this direction such that \(tF\cap \text{int} M\neq \emptyset\) (respectively, \(tF\cap M\neq \emptyset)\). The paper is concerned with various estimates for the minimal cardinality of fixing systems (hindering systems) and the maximal cardinality of primitive fixing systems (primitive hindering systems). Several of the new results are for \(d\)-convex bodies in a Minkowski space \((\mathbb{R}^n\) with a norm).
scientific article; zbMATH DE number 1460296