Characterization of f-vectors of families of convex sets in Rd part II: Sufficiency of Eckhoff's conditions
- Kalai, Gil
DOIAbstract
AbstractLet K = {K1,…, Kn} be a family of n convex sets in Rd. For 0⩽i<n denote by fi the number of subfamilies of K of size i + 1 with non-empty intersection. The vector f(K) = (f0, f1,…) is called the f-vector of K. In 1973, Eckhoff proposed a characterization of the set of f-vectors of finite families of convex sets in Rd by a system of inequalities. In part I we proved the necessity of Eckhoffs inequalities and here we prove their sufficiency
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