关于五维吻合安排的说明

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Research Letters Pub Date : 2024-05-14 DOI:10.4310/mrl.2023.v30.n5.a13

Ferenc Szöllősi

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引用次数: 0

摘要

接吻数 $\tau (d)$ 是指在 $d$ 维欧几里得空间中，每个与中心单位球接触的成对非重叠单位球的最大数目。在这篇论文中，我们报告了如何在 5 美元维度中发现了一种新的、以前未知的 40 个单位球的排列方式。我们的排列使 $\tau (5)$ 的已知最佳下限达到饱和，并反驳了 Cohn-Jiaoo-Kumar-Torquato 的 "信念"。

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A note on five dimensional kissing arrangements

The kissing number $\tau (d)$ is the maximum number of pairwise non-overlapping unit spheres each touching a central unit sphere in the $d$-dimensional Euclidean space. In this note we report on how we discovered a new, previously unknown arrangement of 40 unit spheres in dimension $5$. Our arrangement saturates the best known lower bound on $\tau (5)$, and refutes a ‘belief’ of Cohn–Jiao–Kumar–Torquato.

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来源期刊

Mathematical Research Letters 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6.0 months

期刊介绍： Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.