{
  "id": "1305.6616",
  "version": "v2",
  "published": "2013-05-28T20:03:54.000Z",
  "updated": "2014-07-12T02:38:29.000Z",
  "title": "A refinement of Wilf-equivalence for patterns of length 4",
  "authors": [
    "Jonathan Bloom"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In their paper \\cite{DokosDwyer:Permutat12}, Dokos et al. conjecture that the major index statistic is equidistributed among 1423-avoiding, 2413-avoiding, and 2314-avoiding permutations. In this paper we confirm this conjecture by constructing two major index preserving bijections, $\\Theta:S_n(1423)\\to S_n(2413)$ and $\\Omega:S_n(2314)\\to S_n(2413)$. In fact, we show that $\\Theta$ (respectively, $\\Omega$) preserves numerous other statistics including the descent set, right-to-left maximum (respectively, left-to-right minimum), and a new statistic we call top-steps (respectively, bottom-steps).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-12T02:38:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A19"
    ],
    "keywords": [
      "refinement",
      "wilf-equivalence",
      "major index statistic",
      "major index preserving bijections",
      "left-to-right minimum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.6616B"
    }
  }
}