{
  "id": "1512.08155",
  "version": "v1",
  "published": "2015-12-26T23:40:01.000Z",
  "updated": "2015-12-26T23:40:01.000Z",
  "title": "Pattern avoiding permutations and independent sets in graphs",
  "authors": [
    "Christian Bean",
    "Murray Tannock",
    "Henning Ulfarsson"
  ],
  "comment": "31 pages, 19 figures, 2 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "We encode certain pattern avoiding permutations as weighted independent sets in a family of graphs we call cores. For the classical case of 132-avoiding permutations we establish a bijection between the vertices of the cores and edges in a fully connected graph drawn on a convex polygon. We prove that independent sets in the core correspond to non-crossing subgraphs on the polygon, and then the well-known enumeration of these subgraphs transfers to an enumeration of 132-avoiding permutations according to left-to-right minima. We extend our results to the 123-, (1324, 2143)-, (1234, 1324, 2143)-, (1234, 1324, 1432, 3214)-avoiding permutations. We end by enumerating certain subsets of 1324-avoiding permutations that satisfy particular conditions on their left-to-right minima and right-to-left maxima.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-26T23:40:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "05C69"
    ],
    "keywords": [
      "pattern avoiding permutations",
      "left-to-right minima",
      "well-known enumeration",
      "convex polygon",
      "fully connected graph drawn"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151208155B"
    }
  }
}