Many Collinear $$k$$ k -Tuples with no $$k+1$$ k + 1 Collinear Points
نویسندگان
چکیده
منابع مشابه
Many collinear k-tuples with no k+1 collinear points
For every k > 3, we give a construction of planar point sets with many collinear k-tuples and no collinear (k + 1)-tuples.
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For every k > 3, we give a construction of planar point sets with many collinear k-tuples and no collinear (k + 1)-tuples. We show that there are n0 = n0(k) and c = c(k) such that if n ≥ n0, then there exists a set of n points in the plane that does not contain k + 1 points on a line, but it contains at least n 2− c √ logn collinear k-tuples of points. Thus, we significantly improve the previou...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2013
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-013-9526-9