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 A076523 Maximal number of halving lines for 2n points in plane. 0
 1, 3, 6, 9, 13, 18, 22, 27, 33, 38, 44, 51, 57 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let S be a set of n points in the plane. A halving line is a line through two points in S that splits the remaining points into two equal-sized subsets. How many halving lines can S have? The values n = 8, 9, 10, 11, 12 and 13 were obtained by Abrego et al. The same values hold also for the maximum number of pseudo-halving lines in a generalized configuration of 2n points. The next unknown value, n = 14 (i.e. the maximum number of halving lines among 28 points), is either 63 or 64. - Bernardo M Abrego (bernardo.abrego(AT)csun.edu), May 05 2008 LINKS B. M. Abrego, S. Fernandez-Merchant, J. LeaĆ±os and G. Salazar, The maximum number of halving lines and the rectilinear crossing number of K_n for n <= 27, Electronic Notes in Discrete Mathematics, 30 (2008), 261-266. A. Beygelzimer and S. Radziszowski, On halving line arrangements, Discrete Math., 257 (2002), 267-283. Jeff Erickson, Halving lines and k-sets Tanya Khovanova and Dai Yang, Halving Lines and Their Underlying Graphs, arXiv:1210.4959 [math.CO], 2012. Tanya Khovanova, Dai Yang, Connected Components of Underlying Graphs of Halving Lines, arXiv:1304.5658 [math.CO], 2013. Tanya Khovanova, Dai Yang, Fission of Halving Edges Graphs, arXiv:1310.3510 [math.CO], 2013. Geza Toth, Point sets with many k-sets, in Proceedings of the 16th Annual ACM Symposium on Computational Geometry, 2000, pp. 37-42. CROSSREFS Sequence in context: A032782 A310157 A310158 * A310159 A282720 A129403 Adjacent sequences:  A076520 A076521 A076522 * A076524 A076525 A076526 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Oct 18 2002 EXTENSIONS More terms from Bernardo M Abrego (bernardo.abrego(AT)csun.edu), May 05 2008 STATUS approved

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Last modified December 12 19:33 EST 2018. Contains 318081 sequences. (Running on oeis4.)