On free planes in lattice ball packings

被引：2
|
作者：
Henk, M
Ziegler, GM
Zong, CM
机构：
[1] Univ Magdeburg, Fachbereich Math IMO, D-39106 Magdeburg, Germany
[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
[3] Tech Univ Berlin, Fachbereich Math MA 7 1, D-10623 Berlin, Germany
来源：
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2002年 / 34卷
基金：
中国国家自然科学基金;
关键词：
D O I：
10.1112/S0024609301008888
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This note, by studying the relations between the length of the shortest lattice vectors and the covering minima of a lattice, proves that for every d-dimensional packing lattice of balls one can find a four-dimensional plane, parallel to a lattice plane, such that the plane meets none of the balls of the packing, provided that the dimension d is large enough. Nevertheless, for certain ball packing lattices, the highest dimension of such 'free planes' is far from d.
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页码：284 / 290
页数：7
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