The D4 root system is not universally optimal

被引:19
作者
Cohn, Henry
Conway, John H.
Elkies, Noam D.
Kumar, Abhinav
机构
[1] Microsoft Res, Redmond, WA 98052 USA
[2] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
[3] Harvard Univ, Dept Math, Cambridge, MA 02138 USA
[4] MIT, Dept Math, Cambridge, MA 02139 USA
基金
美国国家科学基金会;
关键词
24-cell; D-4 root system; potential energy minimization; spherical code; spherical design; universally optimal code;
D O I
10.1080/10586458.2007.10129008
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove that the D-4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in S-3, based on numerical computations suggesting that every 5-design consisting of 24 points in S-3 is in a 3-parameter family (which we describe explicitly, based on a construction due to Sali) of deformations of the D-4. root system.
引用
收藏
页码:313 / 320
页数:8
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