{
  "id": "0912.4747",
  "version": "v1",
  "published": "2009-12-23T22:03:09.000Z",
  "updated": "2009-12-23T22:03:09.000Z",
  "title": "Dyck Paths, Standard Young Tableaux, and Pattern Avoiding Permutations",
  "authors": [
    "Hilmar Gudmundsson"
  ],
  "comment": "15 pages, 4 figures. Submitted to a special edition of Pure Mathematics and Applications in 2009. Research supported by grant no. 060005013 from the Icelandic Research Fund",
  "categories": [
    "math.CO"
  ],
  "abstract": "We present a generating function and a closed counting formula in two variables that enumerate a family of classes of permutations that avoid or contain an increasing pattern of length three and have a prescribed number of occurrences of another pattern of length three. This gives a refinement of some previously studied statistics, most notably one by Noonan. The formula is also shown to enumerate a family of classes of Dyck paths and Standard Young Tableaux, and a bijection is given between the corresponding classes of these two families of objects. Finally, the results obtained are used to solve an optimization problem for a certain card game.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-23T22:03:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A19"
    ],
    "keywords": [
      "standard young tableaux",
      "pattern avoiding permutations",
      "dyck paths",
      "optimization problem",
      "card game"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.4747G"
    }
  }
}