{
  "id": "2107.12459",
  "version": "v1",
  "published": "2021-07-26T20:18:39.000Z",
  "updated": "2021-07-26T20:18:39.000Z",
  "title": "The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences",
  "authors": [
    "Altar Çiçeksiz",
    "Yunus Emre Demirci",
    "Ümit Işlak"
  ],
  "comment": "13 pages, 1 figure",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We obtain an explicit formula for the variance of the length of longest $k$-alternating subsequence in a uniformly random permutation. Also a central limit is proved for the same statistic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-26T20:18:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "60F05"
    ],
    "keywords": [
      "alternating subsequence",
      "asymptotic distribution",
      "central limit",
      "uniformly random permutation",
      "explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}