{
  "id": "1007.2946",
  "version": "v2",
  "published": "2010-07-17T18:24:13.000Z",
  "updated": "2014-10-07T22:34:48.000Z",
  "title": "Set families and Foulkes modules",
  "authors": [
    "Mark Wildon",
    "Rowena Paget"
  ],
  "comment": "22 pages, 3 figures, final published version",
  "journal": "Journal of Algebraic Combinatorics 34 (2011) 525-544",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label irreducible characters appearing as summands of the characters of Foulkes modules. The homomorphisms are defined using certain families of subsets of the natural numbers. These families are of independent interest; we prove a number of combinatorial results concerning them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-17T18:24:13.000Z",
      "comment": "22 pages, 3 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-07T22:34:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30",
      "20C15"
    ],
    "keywords": [
      "foulkes modules",
      "set families",
      "homomorphisms",
      "symmetric group",
      "combinatorial results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.2946P"
    }
  }
}