Semidefinite programming bounds for the average kissing number
Maria Dostert (KTH Royal Institute of Technology)
Alexander Kolpakov (Université de Neuchâtel)
Fernando Mário de Oliveira Filho (TU Delft - Discrete Mathematics and Optimization)
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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.