Combinatorial Applications of Cohomology of Toric Varieties
نویسنده
چکیده
1 f-vector for convex polytopes Given a convex polytope P of full dimension in R, we can consider the f-vector, fk = number of k-faces, 0 ≤ k ≤ d− 1. A natural question is Question 1. Given an abstract tuple f of d integers, what are necessary and sufficient conditions for f to be the f-vector of a convex polytope? It turns out to be quite difficult to give sufficient conditions, so let’s determine some necessary ones. First, since P is convex, its boundary is a (d− 1)-sphere, so we have Euler’s relation
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