On Grunbaum's conjecture about inner illumination of convex bodies

被引：1

作者：

Boltyanski, V

Martini, H

Soltan, V

机构：

[1] Ctr Invest Matemat, Guanajuato 36000, Mexico

[2] TU Chemnitz, Fak Math, D-09107 Chemnitz, Germany

[3] George Mason Univ, Dept Math Sci, Fairfax, VA 22030 USA

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 1999年 / 22卷 / 03期

关键词：

Convex Body; Negative Answer; Large Cardinality;

D O I：

10.1007/PL00009468

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In 1964 Grunbaum conjectured that any primitive set illuminating from within a convex body in E-d, d greater than or equal to 3, has at most 2(d) points. This was confirmed by V. Soltan in 1995 for the case d = 3. Here we give a negative answer to Grunbaum's conjecture for all d greater than or equal to 4, by constructing a convex body K subset of E-d with primitive illuminating sets of an arbitrarily large cardinality.

引用

页码：403 / 410

页数：8

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