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Semidefinite programming bounds for the average kissing number

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Abstract

The average kissing number in \({\mathbb{R}^n}\) 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,..., 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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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology (KTH), 10044, Stockholm, Sweden

    Maria Dostert

  2. Institut de mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, 2000, Neuchâtel, Suisse, Switzerland

    Alexander Kolpakov

  3. Delft Institute of Applied Mathematics, Delft University of Technology, Van Mourik Broekmanweg 6, 2628 XE, Delft, The Netherlands

    Fernando Mário de Oliveira Filho

Authors
  1. Maria Dostert
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  2. Alexander Kolpakov
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  3. Fernando Mário de Oliveira Filho
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Corresponding author

Correspondence to Maria Dostert.

Additional information

The second author was supported by the Swiss National Science Foundation project number PP00P2_170560.

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Dostert, M., Kolpakov, A. & de Oliveira Filho, F.M. Semidefinite programming bounds for the average kissing number. Isr. J. Math. 247, 635–659 (2022). https://doi.org/10.1007/s11856-022-2288-4

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

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