{
  "id": "1901.00197",
  "version": "v1",
  "published": "2019-01-01T18:57:44.000Z",
  "updated": "2019-01-01T18:57:44.000Z",
  "title": "Is the Symmetric Group Sperner?",
  "authors": [
    "Larry H. Harper",
    "Gene B. Kim"
  ],
  "comment": "7 pages, 7 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "An antichain A in a poset P is a subset of P in which no two elements are comparable. Sperner showed that the maximal antichain in the Boolean lattice, B_n, is the largest rank (of size n choose n/2). This type of problem has since been generalized, and a graded poset P is said to be Sperner if the largest rank of P is its maximal antichain. In this paper, we will show that the symmetric group S_n, partially ordered by refinement (or equivalently by absolute order), is Sperner.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-01T18:57:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05E99",
      "60F05"
    ],
    "keywords": [
      "symmetric group sperner",
      "maximal antichain",
      "largest rank",
      "boolean lattice",
      "absolute order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}