{
  "id": "1204.2872",
  "version": "v2",
  "published": "2012-04-13T03:42:46.000Z",
  "updated": "2024-09-24T01:50:43.000Z",
  "title": "A Central Limit Theorem for Repeating Patterns",
  "authors": [
    "Aaron Abrams",
    "Eric Babson",
    "Henry Landau",
    "Zeph Landau",
    "James Pommersheim"
  ],
  "comment": "19 pages, 1 figure, 11 references",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each, such as the alternating case considered by Stanley in arXiv:math/0511419 and Widom in arXiv:math/0511533. In every case considered the convergence in the limit of long permutations is to normal with mean and variance linear in the length of the permutation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-13T03:42:46.000Z",
      "abstract": "This note gives a central limit theorem for the length of the longest subsequence of a random permutation which follows some repeating pattern. This includes the case of any fixed pattern of ups and downs which has at least one of each, such as the alternating case considered by Stanley in [2] and Widom in [3]. In every case considered the convergence in the limit of long permutations is to normal with mean and variance linear in the length of the permutations.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2024-09-24T01:50:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16"
    ],
    "keywords": [
      "central limit theorem",
      "repeating pattern",
      "longest subsequence",
      "random permutation",
      "long permutations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2872A"
    }
  }
}