Semidefinite programming bounds for the average kissing number

Journal Article (2022)
Authors

Maria Dostert (KTH Royal Institute of Technology)

Alexander Kolpakov (Université de Neuchâtel)

F.M. De Oliveira Filho (TU Delft - Discrete Mathematics and Optimization)

Research Group
Discrete Mathematics and Optimization
Copyright
© 2022 Maria Dostert, Alexander Kolpakov, F.M. de Oliveira Filho
To reference this document use:
https://doi.org/10.1007/s11856-022-2288-4
More Info
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Publication Year
2022
Language
English
Copyright
© 2022 Maria Dostert, Alexander Kolpakov, F.M. de Oliveira Filho
Research Group
Discrete Mathematics and Optimization
Issue number
2
Volume number
247
Pages (from-to)
635-659
DOI:
https://doi.org/10.1007/s11856-022-2288-4
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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.

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