{
  "id": "2003.11832",
  "version": "v1",
  "published": "2020-03-26T11:00:33.000Z",
  "updated": "2020-03-26T11:00:33.000Z",
  "title": "Semidefinite programming bounds for the average kissing number",
  "authors": [
    "Maria Dostert",
    "Alexander Kolpakov",
    "Fernando Mário de Oliveira Filho"
  ],
  "comment": "17 pages",
  "categories": [
    "math.MG",
    "math.OC"
  ],
  "abstract": "The average kissing number of $\\mathbb{R}^n$ 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 $3, \\ldots, 9$. A very simple upper bound for the average kissing number is twice the kissing number; in dimensions $6, \\ldots, 9$ our new bound is the first to improve on this simple upper bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-26T11:00:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C17",
      "90C22",
      "90C34"
    ],
    "keywords": [
      "average kissing number",
      "semidefinite programming bounds",
      "simple upper bound",
      "contact graphs",
      "dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}