{
  "id": "1707.07195",
  "version": "v1",
  "published": "2017-07-22T17:08:05.000Z",
  "updated": "2017-07-22T17:08:05.000Z",
  "title": "Equidistributions of MAJ and STAT over pattern avoiding permutations",
  "authors": [
    "Joanna N. Chen"
  ],
  "comment": "10 pages",
  "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 $stat$. Recently, Amini investigated the equidistributions of these Mahonian statistics over sets of pattern avoiding permutations. Moreover, he posed several conjectures. In this paper, we construct a bijection from $S_n(213)$ to $S_n(231)$, which maps the statistic $(maj,stat)$ to the statistic $(stat,maj)$. This allows us to give solutions to some of Amini's conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-22T17:08:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pattern avoiding permutations",
      "mahonian statistic",
      "equidistributions",
      "generalized pattern functions",
      "generalized permutation patterns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}