Semidefinite programming bounds for the average kissing number

Dostert, Maria; Kolpakov, Alexander; De Oliveira Filho, F.M.

doi:10.1007/s11856-022-2288-4

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 Discrete Mathematics and Optimization

Research Group

Discrete Mathematics and Optimization

DOI: https://doi.org/10.1007/s11856-022-2288-4

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Published Date

2022

Language

English

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Research Group

Discrete Mathematics and Optimization

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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