{
  "id": "0903.2520",
  "version": "v1",
  "published": "2009-03-14T00:56:44.000Z",
  "updated": "2009-03-14T00:56:44.000Z",
  "title": "On Point Sets in Vector Spaces over Finite Fields That Determine Only Acute Angle Triangles",
  "authors": [
    "Igor E. Shparlinski"
  ],
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "For three points $\\vec{u}$,$\\vec{v}$ and $\\vec{w}$ in the $n$-dimensional space $\\F_q^n$ over the finite field $\\F_q$ of $q$ elements we give a natural interpretation of an acute angle triangle defined by this points. We obtain an upper bound on the size of a set $\\cZ$ such that all triples of distinct points $\\vec{u}, \\vec{v}, \\vec{w} \\in \\cZ$ define acute angle triangles. A similar question in the real space $\\cR^n$ dates back to P. Erd{\\H o}s and has been studied by several authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-14T00:56:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B25",
      "11T23",
      "52C10"
    ],
    "keywords": [
      "finite field",
      "vector spaces",
      "point sets",
      "define acute angle triangles",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.2520S"
    }
  }
}