Semidefinite programming bounds for the average kissing number

Abstract

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 $3,\dots ,9$. A very simple upper bound for the average kissing number is twice the kissing number; in dimensions $6,\dots ,9$ our new bound is the first to improve on this simple upper bound.

17 pages