Tight bounds on a problem of lines and intersections

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Abstract

Consider all arrangements of lines in the plane with r distinct slopes. What is the smallest number of lines f(r) in which there are at least f(r) + 1 points, each defined by the intersection of r lines? We improve the previous lower bound, showing f(r) = Θ(r3). © 1991.

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Sharir, M., & Skiena, S. S. (1991). Tight bounds on a problem of lines and intersections. Discrete Mathematics, 89(3), 313–314. https://doi.org/10.1016/0012-365X(91)90124-K

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