Abstract

The first part of the paper surveys results on f-vectors, flag vectors and h-vectors of convex polytopes. These are combinatorial parameters that have been characterized for simplicial polytopes. Many of the results known in the general case depend on the connection between convex polytopes and toric varieties. The second half of the paper looks at polyhedral subdivisions of convex polytopes. The effect of subdivision on the h-vector is studied. The paper discusses the secondary polytope, which encodes the regular subdivisions of a polytope. Fiber zonotopes and the corresponding hyperplane arrangements, called discriminantal arrangements, are studied.

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