{
  "id": "1412.6473",
  "version": "v1",
  "published": "2014-12-19T18:30:14.000Z",
  "updated": "2014-12-19T18:30:14.000Z",
  "title": "Combinatorics of Tableaux Inversions",
  "authors": [
    "Jonathan E. Beagley",
    "Paul Drube"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A tableaux inversion is a pair of entries in row-standard tableaux $T$ that lie in the same column of $T$ yet lack the appropriate relative ordering to make $T$ column-standard. An $i$-inverted Young tableaux is a row-standard tableaux along with a precisely $i$-inversion pairs. Tableaux inversions were originally introduced by Fresse to calculate the Betti numbers of Springer fibers in Type A, with the number of $i$-inverted tableaux that standardize to a fixed standard Young tableaux corresponding to a specific Betti number of the associated fiber. In this paper we approach the topic of tableaux inversions from a completely combinatorial perspective. We develop formulas enumerating the number of $i$-inverted Young tableaux for a variety of tableaux shapes, not restricting ourselves to inverted tableaux that standardize a specific standard Young tableaux, and construct bijections between $i$-inverted Young tableaux of a certain shape with $j$-inverted Young tableaux of different shapes. Finally, we share some the results of a computer program developed to calculate tableaux inversions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-19T18:30:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tableaux inversion",
      "inverted young tableaux",
      "standard young tableaux corresponding",
      "row-standard tableaux",
      "combinatorics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.6473B"
    }
  }
}