The Division of Space by Hyperplanes with Applications to Geometrical Probability

摘要

Invariant combinatorial properties are investigated of convex cones and their dual cones generated by collections of vectors in a Euclidean space. These properties, which include the number of non-degenerate cones, the number of k-faces of these cones, and the natural measures of the set of k-faces, do not depend on the configuration of the set of generating vectors, except for a weak non-degeneracy requirement. Applications to geometrical probability are given. (Author)