{
  "id": "1109.4624",
  "version": "v2",
  "published": "2011-09-21T19:57:15.000Z",
  "updated": "2012-04-09T12:22:50.000Z",
  "title": "The number of flags in finite vector spaces: Asymptotic normality and Mahonian statistics",
  "authors": [
    "Thomas Bliem",
    "Stavros Kousidis"
  ],
  "comment": "19 pages. Corrected proof of asymptotic normality (Theorem 3.5). Previous Proposition 3.3 is false",
  "journal": "Journal of Algebraic Combinatorics 37 (2013), 361-380",
  "doi": "10.1007/s10801-012-0373-1",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the generalized Galois numbers which count flags of length r in N-dimensional vector spaces over finite fields. We prove that the coefficients of those polynomials are asymptotically Gaussian normally distributed as N becomes large. Furthermore, we interpret the generalized Galois numbers as weighted inversion statistics on the descent classes of the symmetric group on N elements and identify their asymptotic limit as the Mahonian inversion statistic when r approaches infinity. Finally, we apply our statements to derive further statistical aspects of generalized Rogers-Szegoe polynomials, re-interpret the asymptotic behavior of linear q-ary codes and characters of the symmetric group acting on subspaces over finite fields, and discuss implications for affine Demazure modules and joint probability generating functions of descent-inversion statistics.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-09T12:22:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite vector spaces",
      "mahonian statistics",
      "asymptotic normality",
      "generalized galois numbers",
      "symmetric group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.4624B"
    }
  }
}