{
  "id": "1707.01967",
  "version": "v1",
  "published": "2017-07-06T21:15:15.000Z",
  "updated": "2017-07-06T21:15:15.000Z",
  "title": "Signed graphs and the freeness of the Weyl subarrangements of type $B_{\\ell}$",
  "authors": [
    "Daisuke Suyama",
    "Michele Torielli",
    "Shuhei Tsujie"
  ],
  "comment": "29 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A Weyl arrangement is the hyperplane arrangement defined by a root system. Arnold and Saito proved that every Weyl arrangement is free. The Weyl subarrangements of type $A_{\\ell}$ are represented by simple graphs. Stanley gave a characterization of freeness for this type of arrangements in terms of thier graph. In addition, The Weyl subarrangements of type $B_{\\ell}$ can be represented by signed graphs. A characterization of freeness for them is not known. However, characterizations of freeness for a few restricted classes are known. For instance, Edelman and Reiner characterized the freeness of the arrangements between type $ A_{\\ell-1} $ and type $ B_{\\ell} $. In this paper, we give a characterization of the freeness and supersolvability of the Weyl subarrangements of type $B_{\\ell}$ under certain assumption.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-06T21:15:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C35",
      "32S22",
      "05C15",
      "05C22",
      "20F55",
      "13N15"
    ],
    "keywords": [
      "weyl subarrangements",
      "signed graphs",
      "weyl arrangement",
      "characterization",
      "thier graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}