{
  "id": "1201.6243",
  "version": "v3",
  "published": "2012-01-30T15:05:48.000Z",
  "updated": "2014-07-08T09:21:59.000Z",
  "title": "Quadrant marked mesh patterns in 132-avoiding permutations I",
  "authors": [
    "Sergey Kitaev",
    "Jeffrey Remmel",
    "Mark Tiefenbruck"
  ],
  "comment": "Theorem 10 is corrected",
  "journal": "Pure Mathematics and Applications (Pu.M.A.) Vol. 23 (2012), No. 3, pp 219-256",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper is a continuation of the systematic study of the distributions of quadrant marked mesh patterns initiated in [6]. Given a permutation $\\sg = \\sg_1 ... \\sg_n$ in the symmetric group $S_n$, we say that $\\sg_i$ matches the quadrant marked mesh pattern $MMP(a,b,c,d)$ if there are at least $a$ elements to the right of $\\sg_i$ in $\\sg$ that are greater than $\\sg_i$, at least $b$ elements to left of $\\sg_i$ in $\\sg$ that are greater than $\\sg_i$, at least $c$ elements to left of $\\sg_i$ in $\\sg$ that are less than $\\sg_i$, and at least $d$ elements to the right of $\\sg_i$ in $\\sg$ that are less than $\\sg_i$. We study the distribution of $MMP(a,b,c,d)$ in 132-avoiding permutations. In particular, we study the distribution of $MMP(a,b,c,d)$, where only one of the parameters $a,b,c,d$ are non-zero. In a subsequent paper [7], we will study the the distribution of $MMP(a,b,c,d)$ in 132-avoiding permutations where at least two of the parameters $a,b,c,d$ are non-zero.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-08T09:21:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutation",
      "distribution",
      "systematic study",
      "symmetric group",
      "subsequent paper"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}