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A186704
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The minimum number of distinct distances determined by n points in the Euclidean plane.
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1
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0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6
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OFFSET
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1,4
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COMMENTS
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The Mathoverflow link has an image from page 200 of Brass reference.
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REFERENCES
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P. Brass, W. O. J. Moser and J. Pach, Research Problems in Discrete Geometry, Springer (2005), p. 200.
Paul Erdős and Peter Fishburn, Maximum planar sets that determine k distances, Discrete Math. 160:1-3 (1996), pp. 115-125.
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LINKS
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Table of n, a(n) for n=1..13.
L. Guth, N. H. Katz, On the Erdős distinct distance problem in the plane, arXiv:1011.4105 [math.CO]
R. Mansuy, Le problème des distances d'Erdős, Mathematik Park, Institut Henri Poincaré, Paris, 2013.
Mathoverflow, Erdos distance problem n=12
K. Schade, Softwarepraktikum, Sommersemester 2007
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EXAMPLE
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a(4) = a(5) = 2 from the 2 distinct distances between vertices of a square and a regular pentagon.
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CROSSREFS
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Sequence in context: A225559 A082479 A090616 * A067434 A177357 A165906
Adjacent sequences: A186701 A186702 A186703 * A186705 A186706 A186707
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KEYWORD
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nonn,hard,nice
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AUTHOR
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Michael Somos, Feb 25 2011
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STATUS
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approved
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