{
  "id": "math/0206169",
  "version": "v1",
  "published": "2002-06-17T20:54:26.000Z",
  "updated": "2002-06-17T20:54:26.000Z",
  "title": "Some statistics on restricted 132 involutions",
  "authors": [
    "O. Guibert",
    "T. Mansour"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In [GM] Guibert and Mansour studied involutions on n letters avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary pattern on k letters. They also established a bijection between 132-avoiding involutions and Dyck word prefixes of same length. Extending this bijection to bilateral words allows to determine more parameters; in particular, we consider the number of inversions and rises of the involutions onto the words. This is the starting point for considering two different directions: even/odd involutions and statistics of some generalized patterns. Thus we first study generating functions for the number of even or odd involutions on n letters avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary pattern $\\tau$ on k letters. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind. Next, we consider other statistics on 132-avoiding involutions by counting an occurrences of some generalized patterns, related to the enumeration according to the number of rises.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-06-17T20:54:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "statistics",
      "containing",
      "dyck word prefixes",
      "first study generating functions",
      "generalized patterns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......6169G"
    }
  }
}