{
  "id": "1805.00179",
  "version": "v1",
  "published": "2018-05-01T04:10:45.000Z",
  "updated": "2018-05-01T04:10:45.000Z",
  "title": "Characteristic quasi-polynomials of ideals and signed graphs of classical root systems",
  "authors": [
    "Tan Nhat Tran"
  ],
  "comment": "17 pages, we welcome comments",
  "categories": [
    "math.CO"
  ],
  "abstract": "With a main tool is signed graphs, we give a full description of the characteristic quasi-polynomials of ideals of classical root systems ($ABCD$) with respect to the integer and root lattices. As a result, we obtain a full description of the characteristic polynomials of the toric arrangements defined by these ideals. As an application, we provide a combinatorial verification to the fact that the characteristic polynomial of every ideal subarrangement factors over the dual partition of the ideal in the classical cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-01T04:10:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B22",
      "05A18"
    ],
    "keywords": [
      "classical root systems",
      "characteristic quasi-polynomials",
      "signed graphs",
      "characteristic polynomial",
      "full description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}