TY - JOUR
T1 - Characterization of f-vectors of families of convex sets in Rd part II
T2 - Sufficiency of Eckhoff's conditions
AU - Kalai, Gil
PY - 1986/3
Y1 - 1986/3
N2 - Let K = {K1,..., Kn} be a family of n convex sets in Rd. For 0≤ii 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.
AB - Let K = {K1,..., Kn} be a family of n convex sets in Rd. For 0≤ii 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.
UR - http://www.scopus.com/inward/record.url?scp=38249043457&partnerID=8YFLogxK
U2 - 10.1016/0097-3165(86)90079-8
DO - 10.1016/0097-3165(86)90079-8
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AN - SCOPUS:38249043457
SN - 0097-3165
VL - 41
SP - 167
EP - 188
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
IS - 2
ER -