{
  "id": "1212.4187",
  "version": "v1",
  "published": "2012-12-17T22:50:14.000Z",
  "updated": "2012-12-17T22:50:14.000Z",
  "title": "Density theorems for rational numbers",
  "authors": [
    "Andreas Koutsogiannis"
  ],
  "comment": "8 pages. arXiv admin note: text overlap with arXiv:1212.3520",
  "categories": [
    "math.CO"
  ],
  "abstract": "Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic progressions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-17T22:50:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational numbers",
      "density theorems",
      "contain arbitrary long arithmetic progressions",
      "sufficient conditions",
      "measure preserving transformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.4187K"
    }
  }
}