A New Lower Bound Based on Gromov's Method of Selecting Heavily Covered Points

被引：29

作者：

Kral', Daniel ^{[1
]}

Mach, Lukas ^{[1
]}

Sereni, Jean-Sebastien ^{[2
,3
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, Inst Comp Sci, Prague 11800 1, Czech Republic

[2] Univ Paris 07, CNRS, LIAFA, Paris, France

[3] Charles Univ Prague, Fac Math & Phys, Dept Appl Math KAM, Prague 11800 1, Czech Republic

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2012年 / 48卷 / 02期

基金：

欧洲研究理事会;

关键词：

Flag algebras; Covering points by simplicies; Cofilling profiles; Boros-Furedi-Barany-Pach-Gromov theorem;

D O I：

10.1007/s00454-012-9419-3

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Boros and Furedi (for d=2) and Barany (for arbitrary d) proved that there exists a positive real number c (d) such that for every set P of n points in R (d) in general position, there exists a point of R (d) contained in at least d-simplices with vertices at the points of P. Gromov improved the known lower bound on c (d) by topological means. Using methods from extremal combinatorics, we improve one of the quantities appearing in Gromov's approach and thereby provide a new stronger lower bound on c (d) for arbitrary d. In particular, we improve the lower bound on c (3) from 0.06332 to more than 0.07480; the best upper bound known on c (3) being 0.09375.

引用

下载

页码：487 / 498

页数：12

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