一个平面点集的问题

A PROBLEM ON SET OF POINTS IN THE PLANE

平面上有限点集Ｓ与半平面的交称为Ｓ的半空间，恰包含ｋ个点的半空间称为Ｓ的ｋ＿子集，Ｓ的ｋ＿子集的个数记作ｆｋ（Ｓ），令ｆｋ，ｎ＝ｍａｘ｜Ｓ｜＝ｎｆｋ（Ｓ），对ｋ＜ｎ２，本文求得了ｆｋ，ｎ。

For S a set of n point of E 2, the intersection of S and a half_plane is called a semispace of S , A semispace of S of cardinality k is called a k_ subset of S. The number of k_ subsets of S is denoted by f k(S) , Let f k,n = max |S|=nf k (S). In this paper it is proved that f k,n =2k-1kn] for k<n2. .