Person
Frank de Zeeuw
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Related publications (9)
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Distinct distances between points and lines
Frank de Zeeuw, Adrian Claudiu Valculescu, Shakhar Smorodinsky
We show that for m points and n lines in R-2, the number of distinct distances between the points and the lines is Omega(m(1/5)n(3/5)), as long as m(1/2)
Elsevier Science Bv2018On Sets Defining Few Ordinary Circles
An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least ordinary circles. Moreover, we determine the exact minimu ...
Springer2018Distinct Distances on Algebraic Curves in the Plane
Let S be a set of n points in R-2 contained in an algebraic curve C of degree d. We prove that the number of distinct distances determined by S is at least c(d)n(4/3), unless C contains a line or a circle. We also prove the lower bound c(d)' min{m(2/3)n(2/ ...
Cambridge Univ Press2017