A combinatorial perspective on the non-Radon partitions
If (M(E),0) is an oriented matroid without loops defined on a finite set of points E in \({\mathbb{R}}^ d\), then it is uniquely determined by the subsets \(A\subseteq E\) for which there exists a hyperplane strictly separating A from E-A. The author considers the poset of these A's and computes its Möbius function and in a special case its homotopy type. This generalizes results of \textit{P. H. Edelman} on a partial order on regions formed by hyperplanes [Trans. Am. Math. Soc. 283, 617-631 (1984; Zbl 0555.06003)].
scientific article; zbMATH DE number 3910410