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A076523
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Maximal number of halving lines for 2n points in plane.
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0
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1, 3, 6, 9, 13, 18, 22, 27, 33, 38, 44, 51, 57
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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B. M. Abrego, S. Fernandez-Merchant, J. Leaños 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.
T. Khovanova and D, Yang, Halving Lines and Their Underlying Graphs, arXiv preprint arXiv:1210.4959, 2012. - From N. J. A. Sloane, Jan 01 2013
Geza Toth, "Point sets with many k-sets", in Proceedings of the 16th Annual ACM Symposium on Computational Geometry, 2000, pp. 37-42.
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LINKS
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Table of n, a(n) for n=1..13.
Jeff Erickson, Halving lines and k-sets
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CROSSREFS
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Sequence in context: A004131 A171514 A032782 * A129403 A154287 A092847
Adjacent sequences: A076520 A076521 A076522 * A076524 A076525 A076526
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Oct 18 2002
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EXTENSIONS
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More terms from Bernardo M Abrego (bernardo.abrego(AT)csun.edu), May 05 2008
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STATUS
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approved
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