{
  "id": "1812.07112",
  "version": "v1",
  "published": "2018-12-18T00:15:11.000Z",
  "updated": "2018-12-18T00:15:11.000Z",
  "title": "Distributions of Statistics over Pattern-Avoiding Permutations",
  "authors": [
    "Michael Bukata",
    "Ryan Kulwicki",
    "Nicholas Lewandowski",
    "Lara Pudwell",
    "Jacob Roth",
    "Teresa Wheeland"
  ],
  "comment": "26 pages, 2 figures, 4 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider the distribution of ascents, descents, peaks, valleys, double ascents, and double descents over permutations avoiding a set of patterns. Many of these statistics have already been studied over sets of permutations avoiding a single pattern of length 3. However, the distribution of peaks over 321-avoiding permutations is new and we relate it statistics on Dyck paths. We also obtain new interpretations of a number of well-known combinatorial sequences by studying these statistics over permutations avoiding two patterns of length 3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-18T00:15:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05"
    ],
    "keywords": [
      "statistics",
      "pattern-avoiding permutations",
      "distribution",
      "permutations avoiding",
      "well-known combinatorial sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}