{
  "id": "1108.4403",
  "version": "v2",
  "published": "2011-08-22T19:32:53.000Z",
  "updated": "2011-09-15T09:47:57.000Z",
  "title": "Another proof of the $n!$ conjecture",
  "authors": [
    "Geir Ellingsrud",
    "Stein Arild Strømme"
  ],
  "comment": "A referee found a serious flaw in the argument, so we withdraw the paper",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "The \"n! conjecture\" of Garsia and Haiman has inspired mathematicians for nearly two decades, even after Haiman published a proof in 2001. Kumar and Funch Thomsen proved in 2003 that in order to prove the conjecture for all partitions, it suffices to prove it for the so-called \"staircase partitions\" $(k,k-1,...,2,1)$ for each $k>1$. In the present paper we give a construction of a specially designed two-dimensional family of length-$n$ subschemes of the plane, and use that to prove the $n!$ conjecture for staircase partitions. Together with the result of Kumar and Funch Thomsen, this provides a new proof of Haiman's theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-09-15T09:47:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjecture",
      "funch thomsen",
      "staircase partitions",
      "haimans theorem",
      "inspired mathematicians"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.4403E"
    }
  }
}