Restricted Point Configurations with Many Collinear {k}-Tuplets |
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Authors: | Ismailescu |
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Institution: | (1) Department of Mathematics, Hofstra University, Hempstead, NY 11549-1000, USA matdpi@hofstra.edu, US |
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Abstract: |
Abstract. Given k≥ 3 , denote by t'
k
(N) the largest integer for which there is a set of N points in the plane, no k+1 of them on a line such that there are t'
k
(N) lines, each containing exactly k of the points. Erdos (1962) raised the problem of estimating the order of magnitude of t'
k
(N) . We prove that
improving a previous bound of Grunbaum for all k≥ 5 . The proof for k≥ 18 uses an argument of Brass with his permission. |
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Keywords: | |
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