{
  "id": "1806.01525",
  "version": "v1",
  "published": "2018-06-05T07:35:22.000Z",
  "updated": "2018-06-05T07:35:22.000Z",
  "title": "Product formulas for certain skew tableaux",
  "authors": [
    "Jang Soo Kim",
    "Meesue Yoo"
  ],
  "comment": "20 pages, 8 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The hook length formula gives a product formula for the number of standard Young tableaux of a partition shape. The number of standard Young tableaux of a skew shape does not always have a product formula. However, for some special skew shapes, there is a product formula. Recently, Morales, Pak and Panova joint with Krattenthaler conjectured a product formula for the number of standard Young tableaux of shape $\\lambda/\\mu$ for $\\lambda=((2a+c)^{c+a},(a+c)^a)$ and $\\mu=(a+1,a^{a-1},1)$. They also conjectured a product formula for the number of standard Young tableaux of a certain skew shifted shape. In this paper we prove their conjectures using Selberg-type integrals. We also give a generalization of MacMahon's box theorem and a product formula for the trace generating function for a certain skew shape, which is a generalization of a recent result of Morales, Pak and Panova.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-05T07:35:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A30"
    ],
    "keywords": [
      "product formula",
      "standard young tableaux",
      "skew tableaux",
      "hook length formula",
      "macmahons box theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}