%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, <a href="http://compgeom.cs.uiuc.edu/~jeffe/open/ksets.html">
               Halving lines and k-sets</a>
%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