{
  "id": "math/0507314",
  "version": "v2",
  "published": "2005-07-15T12:21:34.000Z",
  "updated": "2005-09-02T11:56:21.000Z",
  "title": "Link complexes of subspace arrangements",
  "authors": [
    "Axel Hultman"
  ],
  "comment": "10 pages; updated reference for Theorem 4.1 (thanks to E. Delucchi)",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "Given a simplicial hyperplane arrangement H and a subspace arrangement A embedded in H, we define a simplicial complex Delta_{A,H} as the subdivision of the link of A induced by H. In particular, this generalizes Steingrimsson's coloring complex of a graph. We do the following: (1) When A is a hyperplane arrangement, Delta_{A,H} is shown to be shellable. As a special case, we answer affirmatively a question of Steingrimsson on coloring complexes. (2) For H being a Coxeter arrangement of type A or B we obtain a close connection between the Hilbert series of the Stanley-Reisner ring of Delta_{A,H} and the characteristic polynomial of A. This extends results of Steingrimsson and provides an interpretation of chromatic polynomials of hypergraphs and signed graphs in terms of Hilbert polynomials.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-09-02T11:56:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F55",
      "14N20"
    ],
    "keywords": [
      "subspace arrangement",
      "link complexes",
      "generalizes steingrimssons coloring complex",
      "simplicial hyperplane arrangement",
      "chromatic polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7314H"
    }
  }
}