Many collinear k - tuples with no k + 1 collinear points József
نویسندگان
چکیده
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 previously best known lower bound for the largest number of collinear k-tuples in such a set, and get reasonably close to the trivial upper bound O(n2).
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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