Semidefinite programming bounds for the average kissing number

Maria Dostert*, Alexander Kolpakov, Fernando Mário de Oliveira Filho

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

The average kissing number in ℝn is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in ℝn. We provide an upper bound for the average kissing number based on semidefinite programming that improves previous bounds in dimensions 3,.., 9. A very simple upper bound for the average kissing number is twice the kissing number; in dimensions 6,.., 9 our new bound is the first to improve on this simple upper bound.

Original languageEnglish
Pages (from-to)635-659
Number of pages25
JournalIsrael Journal of Mathematics
Volume247
Issue number2
DOIs
Publication statusPublished - 2022

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