{
  "id": "1002.2054",
  "version": "v1",
  "published": "2010-02-10T10:05:18.000Z",
  "updated": "2010-02-10T10:05:18.000Z",
  "title": "The number of permutations with k inversions",
  "authors": [
    "Gábor Hegedüs"
  ],
  "comment": "20 pages, submitted to J. of Int. Sequences",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "Let $n\\geq 1$, $0\\leq t\\leq {n \\choose 2}$ be arbitrary integers. Define the numbers $I_n(t)$ as the number of permutations of $[n]$ with $t$ inversions. Let $n,d\\geq 1$ and $0\\leq t\\leq (d-1)n$ be arbitrary integers. Define {\\em the polynomial coefficients} $H(n,d,t)$ as the numbers of compositions of $t$ with at most $n$ parts, no one of which is greater than $d-1$. In our article we give explicit formulas for the numbers $I_n(t)$ and $H(n,d,t)$ using the theory of Gr\\\"obner bases and free resolutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-10T10:05:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "13P10",
      "16E05"
    ],
    "keywords": [
      "inversions",
      "permutations",
      "arbitrary integers",
      "polynomial coefficients",
      "explicit formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.2054H"
    }
  }
}