combinatorial geometry

The generation of combinatorial types of point configurations and hyperplane arrangements point configurations and hyperplane arrangements has long been an outstanding problem of combinatorial geometry.

For the generation of these combinatorial types no direct method is known, and it appears to be necessary to use combinatorial abstractions — allowable sequences of permutations, 𝜆-functions, chirotopes, combinatorial geometries, or oriented matroids; in our work we will use oriented matroids [BLVS⁺99].