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A186704
The minimum number of distinct distances determined by n points in the Euclidean plane.
1
0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6
OFFSET
1,4
COMMENTS
The Mathoverflow link has an image from page 200 of Brass reference.
REFERENCES
P. Brass, W. O. J. Moser and J. Pach, Research Problems in Discrete Geometry, Springer (2005), p. 200.
LINKS
P. Erdős and P. Fishburn, Maximum planar sets that determine k distances, Discrete Math. 160 (1996), 115-125.
L. Guth and N. H. Katz, On the Erdős distinct distance problem in the plane, arXiv:1011.4105 [math.CO], 2010-2011.
R. Mansuy, Le problème des distances d'Erdős, Mathematik Park, Institut Henri Poincaré, Paris, 2013.
EXAMPLE
a(4) = a(5) = 2 from the 2 distinct distances between vertices of a square and a regular pentagon.
CROSSREFS
Sequence in context: A225559 A082479 A090616 * A067434 A336348 A177357
KEYWORD
nonn,hard,more,nice
AUTHOR
Michael Somos, Feb 25 2011
STATUS
approved