{
  "id": "1309.7111",
  "version": "v2",
  "published": "2013-09-27T03:49:04.000Z",
  "updated": "2014-08-23T15:15:22.000Z",
  "title": "Some Wilf-equivalences for vincular patterns",
  "authors": [
    "Andrew M. Baxter",
    "Mark Shattuck"
  ],
  "comment": "20 pages. To appear in the Journal of Combinatorics, Special Issue for the Proceedings of Permutation Patterns 2013",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove several Wilf-equivalences for vincular patterns of length 4, some of which generalize to infinite families of vincular patterns. We also present functional equations for the generating functions for the number of permutations of length n avoiding a single pattern for the patterns 124-3, 134-2, 231-4, 241-3, 132-4, and 142-3. This nearly completes the Wilf-classification of vincular patterns of length 4. As a corollary, these results imply Wilf-equivalences for certain barred patterns of length 5 with a single bar.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-27T03:49:04.000Z",
      "abstract": "We prove several Wilf-equivalences for vincular patterns of length 4, some of which generalize to infinite families of vincular patterns. We also present functional equations for the generating functions for the number of permutations of length n avoiding ? for the patterns 124-3, 134-2, 231-4, 241-3, 132-4, and 142-3. This nearly completes the Wilf-classification of vincular patterns of length 4. As a corollary, these results imply Wilf-equivalences for certain barred patterns of length 5 with a single bar.",
      "comment": "20 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-08-23T15:15:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vincular patterns",
      "single bar",
      "infinite families",
      "results imply wilf-equivalences",
      "functional equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7111B"
    }
  }
}