{
  "id": "1002.1229",
  "version": "v3",
  "published": "2010-02-05T14:20:53.000Z",
  "updated": "2011-02-03T14:44:26.000Z",
  "title": "Centrosymmetric Permutations and Involutions Avoiding 1243 and 2143",
  "authors": [
    "Mark F. Flanagan",
    "Matteo Silimbani"
  ],
  "comment": "25 pages, 8 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A centrosymmetric permutation is one which is invariant under the reverse-complement operation, or equivalently one whose associated standard Young tableaux under the Robinson-Schensted algorithm are both invariant under the Schutzenberger involution. In this paper, we characterize the set of permutations avoiding 1243 and 2143 whose images under the reverse-complement mapping also avoid these patterns. We also characterize in a simple manner the corresponding Schroder paths under a bijection of Egge and Mansour. We then use these results to enumerate centrosymmetric permutations avoiding the patterns 1243 and 2143. In a similar manner, centrosymmetric involutions avoiding these same patterns are shown to be enumerated by the Pell numbers.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-02-03T14:44:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "involutions avoiding",
      "associated standard young tableaux",
      "reverse-complement operation",
      "schutzenberger involution",
      "simple manner"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.1229F"
    }
  }
}