{
  "id": "1003.2728",
  "version": "v3",
  "published": "2010-03-13T17:57:39.000Z",
  "updated": "2010-08-09T00:56:41.000Z",
  "title": "Promotion and evacuation on standard Young tableaux of rectangle and staircase shape",
  "authors": [
    "Steven Pon",
    "Qiang Wang"
  ],
  "comment": "14 pages, typos corrected",
  "categories": [
    "math.CO"
  ],
  "abstract": "(Dual-)promotion and (dual-)evacuation are bijections on SYT(\\lambda) for any partition \\lambda. Let c^r denote the rectangular partition (c,...,c) of height r, and let sc_k (k > 2) denote the staircase partition (k,k-1,...,1). B. Rhoades showed representation-theoretically that promotion on SYT(c^r) exhibits the cyclic sieving phenomenon (CSP). In this paper, we demonstrate a promotion- and evacuation-preserving embedding of SYT(sc_k) into SYT(k^{k+1}). This arose from an attempt to demonstrate the CSP of promotion action on SYT(sc_k).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-08-09T00:56:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "standard young tableaux",
      "staircase shape",
      "evacuation",
      "rectangular partition",
      "staircase partition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.2728P"
    }
  }
}