volume 30, issue 3, P415-435 2003
DOI: 10.1007/s00454-003-2826-8
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Abstract: AbstractLet G be a finite set of points in the plane. A line M is a (k, k)-line, if M is determined by G, and there are at least k points of G in each of the two open half-planes bounded by M . Let f (k, k) denote the maximum size of a set G in the plane, which is not contained in a line and does not determine a (k, k)-line.In this paper we improve previous results of Jaakov Kupitz (, and Micha A. Perles (f (k, k) ≤ 2k + O(log k)). We show that f (k, k) ≤ 2k + O(log log k).

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