{
  "id": "1209.2579",
  "version": "v2",
  "published": "2012-09-12T11:49:10.000Z",
  "updated": "2013-09-09T14:24:19.000Z",
  "title": "Symmetric Chain Decompositions of Quotients of Chain Products by Wreath Products",
  "authors": [
    "Dwight Duffus",
    "Kyle Thayer"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Subgroups of the symmetric group $S_n$ act on powers of chains $C^n$ by permuting coordinates, and induce automorphisms of the ordered sets $C^n$. The quotients defined are candidates for symmetric chain decompositions. We establish this for some families of groups in order to enlarge the collection of subgroups $G$ of the symmetric group $S_n$ for which the quotient $B_n/G$ obtained from the $G$-orbits on the Boolean lattice $B_n$ is a symmetric chain order. The methods are also used to provide an elementary proof that quotients of powers of SCOs by cyclic groups are SCOs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-09T14:24:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A07"
    ],
    "keywords": [
      "symmetric chain decompositions",
      "chain products",
      "wreath products",
      "symmetric group",
      "symmetric chain order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.2579D"
    }
  }
}