|
|
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
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
More terms from Bernardo M Abrego (bernardo.abrego(AT)csun.edu), May 05 2008
|
|
STATUS
|
approved
|
|
|
|