Semidefinite programming bounds for the average kissing number

The average kissing number in ℝ^n is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in 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.