{
  "id": "0911.4823",
  "version": "v5",
  "published": "2009-11-25T11:55:33.000Z",
  "updated": "2010-11-09T13:36:23.000Z",
  "title": "A Tutte polynomial for toric arrangements",
  "authors": [
    "Luca Moci"
  ],
  "comment": "Final version, to appear on Transactions AMS. 28 pages, 4 pictures",
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "We introduce a multiplicity Tutte polynomial M(x,y), with applications to zonotopes and toric arrangements. We prove that M(x,y) satisfies a deletion-restriction recurrence and has positive coefficients. The characteristic polynomial and the Poincare' polynomial of a toric arrangement are shown to be specializations of the associated polynomial M(x,y), likewise the corresponding polynomials for a hyperplane arrangement are specializations of the ordinary Tutte polynomial. Furthermore, M(1,y) is the Hilbert series of the related discrete Dahmen-Micchelli space, while M(x,1) computes the volume and the number of integral points of the associated zonotope.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2010-11-09T13:36:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "toric arrangement",
      "multiplicity tutte polynomial",
      "related discrete dahmen-micchelli space",
      "ordinary tutte polynomial",
      "deletion-restriction recurrence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.4823M"
    }
  }
}