caa a22 4500 469075422 CHVBK 20180323132934.0 cr unu---uuuuu 170328e19920201xx s 000 0 eng 10.1007/BF02187829 doi (NATIONALLICENCE)springer-10.1007/BF02187829 An upper bound on the number of planar K -sets [Elektronische Daten] [János Pach, William Steiger, Endre Szemerédi] 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. Springer-Verlag New York Inc., 1992 Pach János Mathematical Institute, Hungarian Academy of Science, H-1364, Budapest, Hungary aut Steiger William Computer Science Department, Rutgers University, 08903, New Brunswick, NJ, USA aut Szemerédi Endre Mathematical Institute, Hungarian Academy of Science, H-1364, Budapest, Hungary aut Discrete & Computational Geometry Springer New York 7/2(1992-02-01), 109-123 0179-5376 7:2<109 1992 7 454 https://doi.org/10.1007/BF02187829 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02187829 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Pach János Mathematical Institute, Hungarian Academy of Science, H-1364, Budapest, Hungary aut NATIONALLICENCE 700 1- Steiger William Computer Science Department, Rutgers University, 08903, New Brunswick, NJ, USA aut NATIONALLICENCE 700 1- Szemerédi Endre Mathematical Institute, Hungarian Academy of Science, H-1364, Budapest, Hungary aut NATIONALLICENCE 773 0- Discrete & Computational Geometry Springer New York 7/2(1992-02-01), 109-123 0179-5376 7:2<109 1992 7 454 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer