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# Semidefinite programming bounds for the average kissing number

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### 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 $$3, \ldots, 9$$. 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.

### Author and article information

###### Journal
26 March 2020
###### Article
2003.11832