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.
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Elekes, G. A Note on the Number of Distinct Distances. Periodica Mathematica Hungarica 38, 173–177 (1999). https://doi.org/10.1023/A:1004802524095
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DOI: https://doi.org/10.1023/A:1004802524095