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

来源：

EXPERIMENTAL MATHEMATICS | 2007年 / 16卷 / 03期

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

页码：313 / 320

页数：8

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