Abstract
In 1946 P. Erdös posed the problem of determining the minimum numberd(n) of different distances determined by a set ofn points in the Euclidean plane. Erdös provedd(n) ≥cn 1/2 and conjectured thatd(n)≥cn/ √logn. If true, this inequality is best possible as is shown by the lattice points in the plane. We showd(n)≥n 4/5/(logn)c.
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The research of W. T. Trotter was supported in part by the National Science Foundation under DMS 8713994 and DMS 89-02481.
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Chung, F.R.K., Szemerédi, E. & Trotter, W.T. The number of different distances determined by a set of points in the Euclidean plane. Discrete Comput Geom 7, 1–11 (1992). https://doi.org/10.1007/BF02187820
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DOI: https://doi.org/10.1007/BF02187820