Search: id:A076523 Results 1-1 of 1 results found. %I A076523 %S A076523 1,3,6,9,13,18,22,27,33,38,44,51,57 %N A076523 Maximal number of halving lines for 2n points in plane. %C A076523 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? %C A076523 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 %D A076523 A. Beygelzimer and S. Radziszowski, On halving line arrangements, Discrete Math., 257 (2002), 267-283. %D A076523 Geza Toth, "Point sets with many k-sets", in Proceedings of the 16th Annual ACM Symposium on Computational Geometry, 2000, pp. 37-42. %D A076523 B. M. Abrego, S. Fernandez-Merchant, J. Lea[nonascii characters here] 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. %H A076523 Jeff Erickson, Halving lines and k-sets %Y A076523 Sequence in context: A080060 A004131 A032782 this_sequence A129403 A154287 A092847 %Y A076523 Adjacent sequences: A076520 A076521 A076522 this_sequence A076524 A076525 A076526 %K A076523 nonn %O A076523 1,2 %A A076523 N. J. A. Sloane (njas(AT)research.att.com), Oct 18 2002 %E A076523 More terms from Bernardo M Abrego (bernardo.abrego(AT)csun.edu), May 05 2008 Search completed in 0.001 seconds