{
  "id": "1710.04733",
  "version": "v1",
  "published": "2017-10-12T21:49:24.000Z",
  "updated": "2017-10-12T21:49:24.000Z",
  "title": "A poset $Φ_n$ whose maximal chains are in bijection with the $n \\times n$ alternating sign matrices",
  "authors": [
    "Paul Terwilliger"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For an integer $n\\geq 1$, we display a poset $\\Phi_n$ whose maximal chains are in bijection with the $n\\times n$ alternating sign matrices. The Hasse diagram $\\widehat \\Phi_n$ is obtained from the $n$-cube by adding some edges. We show that the dihedral group $D_{2n}$ acts on $\\widehat \\Phi_n$ as a group of automorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-12T21:49:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B20"
    ],
    "keywords": [
      "alternating sign matrices",
      "maximal chains",
      "hasse diagram",
      "dihedral group",
      "automorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}