Abstract
Given a setS ofn points, a subsetX of sizek is called ak-set if there is a hyperplane ? that separatesX fromS?X. We prove thatO(n?k/log*k) is an upper bound for the number ofk-sets in the plane, thus improving the previous bound of Erdos, Lovasz, Simmons, and Strauss by a factor of log*k.
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