{
  "id": "1301.6796",
  "version": "v1",
  "published": "2013-01-28T22:14:20.000Z",
  "updated": "2013-01-28T22:14:20.000Z",
  "title": "Beyond alternating permutations: Pattern avoidance in Young diagrams and tableaux",
  "authors": [
    "Nihal Gowravaram",
    "Ravi Jagadeesan"
  ],
  "comment": "49 pages; comments are welcomed",
  "categories": [
    "math.CO"
  ],
  "abstract": "We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particular, we extend Babson-West's notion of shape-Wilf equivalence to apply to alternating permutations and so generalize results of Backelin-West-Xin and Ouchterlony to alternating permutations. Second, we study pattern avoidance in the more general context of permutations with restricted ascents and descents. We consider a question of Lewis regarding permutations that are the reading words of thickened staircase Young tableaux, that is, permutations that have (k - 1) ascents followed by a descent, followed by (k - 1) ascents, et cetera. We determine the relative sizes of the sets of pattern-avoiding (k - 1)-ascent permutations in terms of the forbidden pattern. Furthermore, we give inequalities in the sizes of sets of pattern-avoiding permutations in this context that arise from further extensions of shape-equivalence type enumerations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-28T22:14:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A19"
    ],
    "keywords": [
      "alternating permutations",
      "young diagrams",
      "study pattern avoidance",
      "shape-equivalence type enumerations",
      "extend babson-wests notion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.6796G"
    }
  }
}