A Note on the Number of Distinct Distances

G. Elekes

doi:10.1023/a:1004802524095

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 38: Issue 3

A Note on the Number of Distinct Distances

Author: G. Elekes¹

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¹ Eötvös Loránd University Budapest Hungary Budapest Hungary

DOI:: https://doi.org/10.1023/a:1004802524095

Page Count:: 173–177

Publication Date:: 01 Jul 1999

Online Publication Date:: 02 Nov 2004

Article Category:: Research Article

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Abstract

We refine a method introduced in [1] and [2] for studying the number of distinct values taken by certain polynomials of two real variables on Cartesian products. We apply it to prove a "gap theorem", improving a recent lower bound on the number of distinct distances between two collinear point sets in the Euclidean space.