Distinct Distances from Three Points-Reference-Cited by-同舟云学术

Distinct Distances from Three Points

Published:2015-09-30 Issue:4 Volume:25 Page:623-632
ISSN:0963-5483
Container-title:Combinatorics, Probability and Computing
language:en
Short-container-title:Combinator. Probab. Comp.

Author:

SHARIR MICHA,SOLYMOSI JÓZSEF

Abstract

Let p1, p2, p3 be three noncollinear points in the plane, and let P be a set of n other points in the plane. We show that the number of distinct distances between p1, p2, p3 and the points of P is Ω(n6/11), improving the lower bound Ω(n0.502) of Elekes and Szabó [4] (and considerably simplifying the analysis).

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science

Reference9 articles.

1. Crossing Numbers and Hard Erdős Problems in Discrete Geometry

2. Pach J. and de Zeeuw F. (2014) Distinct distances on algebraic curves in the plane. In Proc. 30th Symposium on Computational Geometry, pp. 549–557. Also in arXiv:1308.0177.

3. Elekes G. (2002) Sums versus products in number theory, algebra and Erdős geometry: A survey. In Paul Erdős and his Mathematics II, Vol. 11 of Bolyai Mathematical Society Studies, Budapest, pp. 241–290.

4. Distinct distances on two lines

5. A Combinatorial Problem on Polynomials and Rational Functions

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