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https://open.uns.ac.rs/handle/123456789/8642
Title: | Many Collinear k-Tuples with no k+1 Collinear Points | Authors: | Solymosi J. Stojaković, Miloš |
Issue Date: | 1-Oct-2013 | Journal: | Discrete and Computational Geometry | Abstract: | 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 n2-(c√/ log n) 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). © 2013 Springer Science+Business Media New York. | URI: | https://open.uns.ac.rs/handle/123456789/8642 | ISSN: | 01795376 | DOI: | 10.1007/s00454-013-9526-9 |
Appears in Collections: | PMF Publikacije/Publications |
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