{
  "id": "1704.07104",
  "version": "v1",
  "published": "2017-04-24T09:18:17.000Z",
  "updated": "2017-04-24T09:18:17.000Z",
  "title": "Equivalence classes of mesh patterns with a dominating pattern",
  "authors": [
    "Murray Tannock",
    "Henning Ulfarsson"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Two mesh patterns are coincident if they are avoided by the same set of permutations, and are Wilf-equivalent if they have the same number of avoiders of each length. We provide sufficient conditions for coincidence of mesh patterns, when only permutations also avoiding a longer classical pattern are considered. Using these conditions we completely classify coincidences between families containing a mesh pattern of length 2 and a classical pattern of length 3. Furthermore, we completely Wilf-classify mesh patterns of length 2 inside the class of 231-avoiding permutations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-24T09:18:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15"
    ],
    "keywords": [
      "equivalence classes",
      "dominating pattern",
      "permutations",
      "sufficient conditions",
      "wilf-classify mesh patterns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}