Semidefinite programming bounds for the average kissing number

Maria Dostert; Alexander Kolpakov; Fernando Mário de Oliveira Filho

doi:10.1007/s11856-022-2288-4

Semidefinite programming bounds for the average kissing number

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

^*Corresponding author for this work

Discrete Mathematics and Optimization

Research output: Contribution to journal › Article › Scientific › peer-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 language	English
Pages (from-to)	635-659
Number of pages	25
Journal	Israel Journal of Mathematics
Volume	247
Issue number	2
DOIs	https://doi.org/10.1007/s11856-022-2288-4
Publication status	Published - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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title = "Semidefinite programming bounds for the average kissing number",

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.",

author = "Maria Dostert and Alexander Kolpakov and {de Oliveira Filho}, {Fernando M{\'a}rio}",

note = "Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.",

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Semidefinite programming bounds for the average kissing number

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