{
  "id": "math/9405218",
  "version": "v1",
  "published": "1994-05-13T00:00:00.000Z",
  "updated": "1994-05-13T00:00:00.000Z",
  "title": "Average kissing numbers for non-congruent sphere packings",
  "authors": [
    "Greg Kuperberg",
    "Oded Schramm"
  ],
  "comment": "6 pages",
  "journal": "Math.Res.Lett.1:339-344,1994",
  "categories": [
    "math.MG"
  ],
  "abstract": "The Koebe circle packing theorem states that every finite planar graph can be realized as the nerve of a packing of (non-congruent) circles in R^3. We investigate the average kissing number of finite packings of non-congruent spheres in R^3 as a first restriction on the possible nerves of such packings. We show that the supremum k of the average kissing number for all packings satisfies 12.566 ~ 666/53 <= k < 8 + 4*sqrt(3) ~ 14.928 We obtain the upper bound by a resource exhaustion argument and the upper bound by a construction involving packings of spherical caps in S^3. Our result contradicts two naive conjectures about the average kissing number: That it is unbounded, or that it is supremized by an infinite packing of congruent spheres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1994-05-13T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "average kissing number",
      "non-congruent sphere packings",
      "upper bound",
      "koebe circle packing theorem states",
      "resource exhaustion argument"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.4310/MRL.1994.v1.n3.a5"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 391176,
      "adsabs": "1994math......5218K"
    }
  }
}