Equilateral dimension of the rectilinear space

被引：15
作者：
Koolen, J [1 ]
Laurent, M [1 ]
Schrijver, A [1 ]
机构：
[1] Ctr Wiskunde & Informat, NL-1098 SJ Amsterdam, Netherlands
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2000年 / 21卷 / 1-3期
关键词：
touching number; rectilinear space; equidistant set; cut metric; design; touching simplices;
D O I：
10.1023/A:1008391712305
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
It is conjectured that there exist at most 2k equidistant points in the k-dimensional rectilinear space. This conjecture has been verified for k less than or equal to 3; we show here its validity in dimension k = 4. We also discuss a number of related questions. For instance, what is the maximum number of equidistant points lying in the hyperplane: Sigma (k)(i=1) x(i) = 0? If this number would be equal to k, then the above conjecture would follow. We show, however, that this number is greater than or equal to k + 1 for k greater than or equal to 4.
引用
收藏
页码：149 / 164
页数：16
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