{
  "id": "1611.05775",
  "version": "v1",
  "published": "2016-11-17T16:42:08.000Z",
  "updated": "2016-11-17T16:42:08.000Z",
  "title": "Explicit (Polynomial!) Expressions for the Expectation, Variance and Higher Moments of the Size of a (2n + 1, 2n + 3)-core partition with Distinct Parts",
  "authors": [
    "Anthony Zaleski",
    "Doron Zeilberger"
  ],
  "comment": "20 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Inspired by Armin Straub's conjecture (arXiv:1601.07161) about the number and maximal size of (2n+1, 2n+3)-core partitions with distinct parts, we develop relatively efficient, symbolic-computational algorithms, based on non-linear functional recurrences, to generate the generating functions, according to size, of the set of such partitions. By computing these polynomials for n=1,...21, we are able to rigorously derive explicit expressions for the expectation, variance, and third through seventh moments of the random variable \"size of a (2n+1, 2n+3)-core partition with distinct parts.\" In particular, we find that this random variable is not asymptotically normal as n goes to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-17T16:42:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "05A15",
      "05A16",
      "05E10"
    ],
    "keywords": [
      "distinct parts",
      "higher moments",
      "expectation",
      "polynomial",
      "armin straubs conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}