{
  "id": "math/0302301",
  "version": "v1",
  "published": "2003-02-25T09:31:11.000Z",
  "updated": "2003-02-25T09:31:11.000Z",
  "title": "Permutation Statistics on the Alternating Group",
  "authors": [
    "Amitai Regev",
    "Yuval Roichman"
  ],
  "comment": "45 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $A_n\\subseteq S_n$ denote the alternating and the symmetric groups on $1,...,n$. MacMahaon's theorem, about the equi-distribution of the length and the major indices in $S_n$, has received far reaching refinements and generalizations, by Foata, Carlitz, Foata-Schutzenberger, Garsia-Gessel and followers. Our main goal is to find analogous statistics and identities for the alternating group $A_{n}$. A new statistic for $S_n$, {\\it the delent number}, is introduced. This new statistic is involved with new $S_n$ equi-distribution identities, refining some of the results of Foata-Schutzenberger and Garsia-Gessel. By a certain covering map $f:A_{n+1}\\to S_n$, such $S_n$ identities are `lifted' to $A_{n+1}$, yielding the corresponding $A_{n+1}$ equi-distribution identities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-02-25T09:31:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A19"
    ],
    "keywords": [
      "alternating group",
      "permutation statistics",
      "equi-distribution identities",
      "received far reaching refinements",
      "major indices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2301R"
    }
  }
}