{
  "id": "2209.13633",
  "version": "v1",
  "published": "2022-09-27T19:00:11.000Z",
  "updated": "2022-09-27T19:00:11.000Z",
  "title": "Perforated Tableaux in Type $A_{n-1}$ Crystal Graphs and the RSK Correspondence",
  "authors": [
    "Glenn D. Appleby",
    "Tamsen Whitehead"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We continue work begun in \\cite{ptab} which introduced \\emph{perforated tableaux} as a combinatorial model for crystals of type $A_{n-1}$, emphasizing connections to the classical Robinson-Schensted-Knuth (RSK) correspondence and Lusztig involutions, and, more generally, exploring the role of insertion schemes in the analysis of crystal graphs. An essential feature of our work is the role of \\emph{dual} crystals (\\cite{GerberLecouvey,vanLeeuwen}) from which we obtain new results within and beyond the classic RSK theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-27T19:00:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10"
    ],
    "keywords": [
      "crystal graphs",
      "rsk correspondence",
      "perforated tableaux",
      "continue work begun",
      "classic rsk theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}