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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.

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          Author and article information

          Journal
          26 March 2020
          Article
          2003.11832

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          52C17, 90C22, 90C34
          17 pages
          math.MG math.OC

          Numerical methods, Geometry & Topology

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