Sets with few distinct distances do not have heavy lines

被引：11

作者：

Raz, Orit E. ^{[1
]}

Roche-Newton, Oliver ^{[2
]}

Sharir, Micha ^{[1
]}

机构：

[1] Tel Aviv Univ, Sch Comp Sci, IL-69978 Tel Aviv, Israel

[2] Johann Radon Inst Computat & Appl Math, A-4040 Linz, Austria

来源：

DISCRETE MATHEMATICS | 2015年 / 338卷 / 08期

基金：

美国国家科学基金会; 奥地利科学基金会;

关键词：

Incidences; Distinct distances;

D O I：

10.1016/j.disc.2015.02.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let P be a set of n points in the plane that determines at most n/5 distinct distances. We show that no line can contain more than O(n(43/52)polylog(n)) points of P. We also show a similar result for rectangular distances, equivalent to distances in the Minkowski plane, where the distance between a pair of points is the area of the axis-parallel rectangle that they span. (C) 2015 Elsevier BM. All rights reserved.

引用

页码：1484 / 1492

页数：9

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