{
  "id": "1511.04989",
  "version": "v1",
  "published": "2015-11-16T15:36:00.000Z",
  "updated": "2015-11-16T15:36:00.000Z",
  "title": "Corners in tree-like tableaux",
  "authors": [
    "Pawel Hitczenko",
    "Amanda Lohss"
  ],
  "comment": "3 figures",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "In this paper, we study tree--like tableaux, combinatorial objects which exhibit a natural tree structure and are connected to the partially asymmetric simple exclusion process (PASEP). There was a conjecture made on the total number of corners in tree--like tableaux and the total number of corners in symmetric tree--like tableaux. In this paper, we prove both conjectures. Our proofs are based off of the bijection with permutation tableaux or type--B permutation tableaux and consequently, we also prove results for these tableaux. In addition, we derive the limiting distribution of the number of occupied corners in random tree--like tableaux and random symmetric tree--like tableaux.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-16T15:36:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "60C05",
      "60F05"
    ],
    "keywords": [
      "total number",
      "partially asymmetric simple exclusion process",
      "random symmetric tree-like tableaux",
      "natural tree structure",
      "type-b permutation tableaux"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151104989H"
    }
  }
}