{
  "id": "math/0304429",
  "version": "v3",
  "published": "2003-04-27T18:23:37.000Z",
  "updated": "2004-01-12T20:46:46.000Z",
  "title": "Equidistribution and Sign-Balance on 321-Avoiding Permutations",
  "authors": [
    "Ron M. Adin",
    "Yuval Roichman"
  ],
  "comment": "17 pages; to appear in S\\'em. Lothar. Combin",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $T_n$ be the set of 321-avoiding permutations of order $n$. Two properties of $T_n$ are proved: (1) The {\\em last descent} and {\\em last index minus one} statistics are equidistributed over $T_n$, and also over subsets of permutations whose inverse has an (almost) prescribed descent set. An analogous result holds for Dyck paths. (2) The sign-and-last-descent enumerators for $T_{2n}$ and $T_{2n+1}$ are essentially equal to the last-descent enumerator for $T_n$. The proofs use a recursion formula for an appropriate multivariate generating function.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-01-12T20:46:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutations",
      "sign-balance",
      "equidistribution",
      "appropriate multivariate generating function",
      "dyck paths"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4429A"
    }
  }
}