{
  "id": "1701.08044",
  "version": "v1",
  "published": "2017-01-27T13:10:40.000Z",
  "updated": "2017-01-27T13:10:40.000Z",
  "title": "A new bijective proof of Babson and Steingrímsson's conjecture",
  "authors": [
    "Joanna N. Chen",
    "Shouxiao Li"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Babson and Steingr\\'{\\i}msson introduced generalized permutation patterns and showed that most of the Mahonian statistics in the literature can be expressed by the combination of generalized pattern functions. Particularly, they defined a new Mahonian statistic in terms of generalized pattern functions, which is denoted $stat$. Given a permutation $\\pi$, let $des(\\pi)$ denote the descent number of $\\pi$ and $maj(\\pi)$ denote the major index of $\\pi$. Babson and Steingr\\'{\\i}msson conjectured that $(des,stat)$ and $(des,maj)$ are equidistributed on $S_n$. Foata and Zeilberger settled this conjecture using q-enumeration, generating functions and Maple packages ROTA and PERCY. Later, Burstein provided a bijective proof of a refinement of this conjecture. In this paper, we give a new bijective proof of this conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-27T13:10:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bijective proof",
      "steingrímssons conjecture",
      "mahonian statistic",
      "generalized pattern functions",
      "maple packages rota"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}