{
  "id": "math/0509174",
  "version": "v2",
  "published": "2005-09-07T23:26:14.000Z",
  "updated": "2005-10-03T21:12:16.000Z",
  "title": "Properties of four partial orders on standard Young tableaux",
  "authors": [
    "Muge Taskin"
  ],
  "comment": "24 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let SYT_n be the set of all standard Young tableaux with n cells. After recalling the definitions of four partial orders, the weak, KL, geometric and chain orders on SYT_n and some of their crucial properties, we prove three main results: (i)Intervals in any of these four orders essentially describe the product in a Hopf algebra of tableaux defined by Poirier and Reutenauer. (ii) The map sending a tableau to its descent set induces a homotopy equivalence of the proper parts of all of these orders on tableaux with that of the Boolean algebra 2^{[n-1]}. In particular, the M\\\"obius function of these orders on tableaux is (-1)^{n-3}. (iii) For two of the four orders, one can define a more general order on skew tableaux having fixed inner boundary, and similarly analyze their homotopy type and M\\\"obius function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-10-03T21:12:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "standard young tableaux",
      "partial orders",
      "properties",
      "descent set induces",
      "main results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9174T"
    }
  }
}