{
  "id": "1206.2885",
  "version": "v2",
  "published": "2012-06-13T17:57:59.000Z",
  "updated": "2014-07-03T16:24:55.000Z",
  "title": "A Probabilistic Threshold for Monochromatic Arithmetic Progressions",
  "authors": [
    "Aaron Robertson"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that $\\sqrt{k}\\cdot r^{k/2}$ is a threshold interval length where, under mild conditions, almost every $r$-coloring of an interval of longer length contains a monochromatic $k$-term arithmetic progression, while almost no $r$-coloring of an interval of shorter length contains a monochromatic $k$-term arithmetic progression.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-03T16:24:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10"
    ],
    "keywords": [
      "monochromatic arithmetic progressions",
      "probabilistic threshold",
      "term arithmetic progression",
      "threshold interval length",
      "shorter length contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.2885R"
    }
  }
}