{
  "id": "1908.01382",
  "version": "v1",
  "published": "2019-08-04T18:24:17.000Z",
  "updated": "2019-08-04T18:24:17.000Z",
  "title": "Permutations avoiding a certain pattern of length three under Mallows distributions",
  "authors": [
    "Ross G. Pinsky"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider permutations avoiding a certain pattern of length three under the family of Mallows distributions. In particular, we obtain rather precise bounds on the asymptotic probability as $n\\to\\infty$ that a permutation $\\sigma\\in S_n$ under the Mallows distribution with parameter $q\\in(0,1)$ avoids the pattern 312. The same result also holds for permutations avoiding 231. And by a duality, the same type of result also holds for the pattern 213 or 132 under the Mallows distribution with parameter $q>1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-04T18:24:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "05A05"
    ],
    "keywords": [
      "mallows distribution",
      "permutations avoiding",
      "asymptotic probability",
      "precise bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}