{
  "id": "0912.2387",
  "version": "v3",
  "published": "2009-12-12T01:26:54.000Z",
  "updated": "2011-01-30T04:07:47.000Z",
  "title": "A generalization of Larman-Rogers-Seidel's theorem",
  "authors": [
    "Hiroshi Nozaki"
  ],
  "comment": "12 pages, no figure",
  "categories": [
    "math.MG",
    "math.CO"
  ],
  "abstract": "A finite set X in the d-dimensional Euclidean space is called an s-distance set if the set of Euclidean distances between any two distinct points of X has size s. Larman--Rogers--Seidel proved that if the cardinality of a two-distance set is greater than 2d+3, then there exists an integer k such that a^2/b^2=(k-1)/k, where a and b are the distances. In this paper, we give an extension of this theorem for any s. Namely, if the size of an s-distance set is greater than some value depending on d and s, then certain functions of s distances become integers. Moreover, we prove that if the size of X is greater than the value, then the number of s-distance sets is finite.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-01-30T04:07:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51K05",
      "05B25"
    ],
    "keywords": [
      "larman-rogers-seidels theorem",
      "s-distance set",
      "generalization",
      "d-dimensional euclidean space",
      "finite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.2387N"
    }
  }
}