An upper bound on the number of planarK-sets
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- Pach, J., Steiger, W. & Szemerédi, E. Discrete Comput Geom (1992) 7: 109. doi:10.1007/BF02187829
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Given a setS ofn points, a subsetX of sizek is called ak-set if there is a hyperplane Π 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 Erdös, Lovász, Simmons, and Strauss by a factor of log*k.