{
  "id": "0707.0213",
  "version": "v1",
  "published": "2007-07-02T12:51:23.000Z",
  "updated": "2007-07-02T12:51:23.000Z",
  "title": "Unit distances and diameters in Euclidean spaces",
  "authors": [
    "Konrad J Swanepoel"
  ],
  "journal": "Discrete and Computational Geometry 49 (2009), 1--27.",
  "doi": "10.1007/s00454-008-9082-x",
  "categories": [
    "math.MG",
    "math.CO"
  ],
  "abstract": "We show that the maximum number of unit distances or of diameters in a set of n points in d-dimensional Euclidean space is attained only by specific types of Lenz constructions, for all d >= 4 and n sufficiently large, depending on d. As a corollary we determine the exact maximum number of unit distances for all even d >= 6, and the exact maximum number of diameters for all d >= 4, for all $n$ sufficiently large, depending on d.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-02T12:51:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C10"
    ],
    "keywords": [
      "unit distances",
      "exact maximum number",
      "sufficiently large",
      "d-dimensional euclidean space",
      "specific types"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.0213S"
    }
  }
}