{
  "id": "1107.1098",
  "version": "v2",
  "published": "2011-07-06T11:21:29.000Z",
  "updated": "2011-08-26T15:21:02.000Z",
  "title": "Some Quotients of the Boolean Lattice are Symmetric Chain Orders",
  "authors": [
    "Dwight Duffus",
    "Jeremy McKibben-Sanders",
    "Kyle Thayer"
  ],
  "comment": "The significant changes from the first version are: inclusion of Theorem 3 and Corollary 1, with the proof of the former in Section 5. Small corrections and rewordings have been done as well",
  "categories": [
    "math.CO"
  ],
  "abstract": "R. Canfield has conjectured that for all subgroups G of the automorphism group of the Boolean lattice B(n) (which can be regarded as the symmetric group S(n)) the quotient order B(n)/G is a symmetric chain order. We provide a straightforward proof of a generalization of a result of K. K. Jordan: namely, B(n)/G is an SCO whenever G is generated by powers of disjoint cycles. The symmetric chain decompositions of Greene and Kleitman provide the basis for partitions of these quotients.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-08-26T15:21:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A07",
      "05E18"
    ],
    "keywords": [
      "symmetric chain order",
      "boolean lattice",
      "symmetric chain decompositions",
      "quotient order",
      "symmetric group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.1098D"
    }
  }
}