{
  "id": "1508.05293",
  "version": "v1",
  "published": "2015-08-21T14:57:08.000Z",
  "updated": "2015-08-21T14:57:08.000Z",
  "title": "Strange Expectations",
  "authors": [
    "Marko Thiel",
    "Nathan Williams"
  ],
  "comment": "31 pages, 3 figures",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "Let gcd(a,b)=1. J. Olsson and D. Stanton proved that the maximum number of boxes in a simultaneous (a,b)-core is (a^2-1)(b^2-1)/24, and that this maximum was achieved by a unique core. P. Johnson combined Ehrhart theory with the polynomial method to prove D. Armstrong's conjecture that the expected number of boxes in a simultaneous (a,b)-core is (a-1)(b-1)(a+b+1)/24. We extend P. Johnson's method to compute the variance to be ab(a-1)(b-1)(a+b)(a+b+1)/1440. By extending the definitions of \"simultaneous cores\" and \"number of boxes\" to affine Weyl groups, we give uniform generalizations of all three formulae above to simply-laced affine types. We further explain the appearance of the number 24 using the \"strange formula\" of H. Freudenthal and H. de Vries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-21T14:57:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E99"
    ],
    "keywords": [
      "strange expectations",
      "affine weyl groups",
      "maximum number",
      "simply-laced affine types",
      "unique core"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150805293T"
    }
  }
}