{
  "id": "1101.5071",
  "version": "v2",
  "published": "2011-01-26T14:47:11.000Z",
  "updated": "2011-04-22T16:57:50.000Z",
  "title": "On bar lengths in partitions",
  "authors": [
    "Jean-Baptiste Gramain",
    "Jorn B. Olsson"
  ],
  "journal": "Proceedings of the Edinburgh Mathematical Society, Vol 55 (2012), 1-16",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "In this paper, we present, given a odd integer $d$, a decomposition of the multiset of bar lengths of a bar partition $\\lambda$ as the union of two multisets, one consisting of the bar lengths in its $\\bar{d}$-core partition $\\bar{c}_d(\\lambda)$ and the other consisting of modified bar lengths in its $\\bar{d}$-quotient partition. In particular, we obtain that the multiset of bar lengths in $\\bar{c}_d(\\lambda)$ is a sub-multiset of the multiset of bar lengths in $\\lambda$. Also we obtain a relative bar formula for the degrees of spin characters of the Schur extensions of the symmetric group. The proof involves a recent similar result for partitions, proved in [1].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-22T16:57:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30",
      "20C15",
      "20C20"
    ],
    "keywords": [
      "odd integer",
      "core partition",
      "modified bar lengths",
      "similar result",
      "bar partition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}