论文标题
平均接吻号的半决赛编程界限
Semidefinite programming bounds for the average kissing number
论文作者
论文摘要
$ \ mathbb {r}^n $的平均接吻数是有限的许多球（任何RADII）的平均接触度的至高无上的至高无上。我们为基于半决赛编程的平均亲吻号提供了上限，该界限改善了尺寸的先前界限$ 3，\ ldots，9 $。平均接吻号的非常简单的上限是接吻号的两倍。在尺寸中，$ 6，\ ldots，9 $我们的新界限是第一个在这个简单的上限上改进的界限。
The average kissing number of $\mathbb{R}^n$ is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in $\mathbb{R}^n$. We provide an upper bound for the average kissing number based on semidefinite programming that improves previous bounds in dimensions $3, \ldots, 9$. A very simple upper bound for the average kissing number is twice the kissing number; in dimensions $6, \ldots, 9$ our new bound is the first to improve on this simple upper bound.
