Odd strength spherical designs attaining the Fazekas–Levenshtein bound for covering and universal minima of potentials

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-03-06 DOI:10.1007/s00010-024-01036-6

Sergiy Borodachov

引用次数: 0

Abstract

We characterize the cases of existence of spherical designs of an odd strength attaining the Fazekas–Levenshtein bound for covering and prove some of their properties. We also find all universal minima of the potential of regular spherical configurations in two new cases: the demihypercube on \(S^d\), \(d\ge 4\), and the \(2_{41}\) polytope on \(S^7\) (which is dual to the \(E_8\) lattice).

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奇数强度球形设计达到法泽卡斯-列文斯丹边界的覆盖和普遍最小电位

我们描述了达到法泽卡斯-列文森斯坦（Fazekas-Levenshtein）覆盖边界的奇数强度球形设计的存在情况，并证明了它们的一些性质。我们还发现了两种新情况下规则球形配置的势的所有普遍最小值：\(S^d\)上的\(d\ge 4\) 半超立方体，以及\(S^7\)上的\(2_{41}\)多面体（它与\(E_8\)网格是对偶的）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.