Hyperplane arrangement

Summary

A hyperplane arrangement is a finite set of hyperplanes in a vector space or affine space. Over the real numbers the hyperplanes cut the space into convex pieces called regions. One studies how many regions there are and how they fit together. The combinatorics of an arrangement is captured by its intersection poset, the partially ordered set of all nonempty intersections of its hyperplanes. Arrangements connect polytopes, matroids, root systems and the topology of complements of hypersurfaces.