{
  "id": "math/0109205",
  "version": "v1",
  "published": "2001-09-26T01:58:11.000Z",
  "updated": "2001-09-26T01:58:11.000Z",
  "title": "On counting permutations by pairs of congruence classes of major index",
  "authors": [
    "Helene Barcelo",
    "Robert Maule",
    "Sheila Sundaram"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a fixed positive integer n, let S_n denote the symmetric group of n! permutations on n symbols, and let maj(sigma) denote the major index of a permutation sigma. For positive integers k<m not greater than n and non-negative integers i and j, we give enumerative formulas for the cardinality of the set of permutations sigma in S_n with maj(sigma) congruent to i mod k and maj(sigma^(-1)) congruent to j mod m. When m divides n-1 and k divides n, we show that for all i,j, this cardinality equals (n!)/(km).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-09-26T01:58:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A99",
      "05E99"
    ],
    "keywords": [
      "major index",
      "congruence classes",
      "counting permutations",
      "positive integer",
      "symmetric group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......9205B"
    }
  }
}