{
  "id": "0711.4382",
  "version": "v6",
  "published": "2007-11-28T20:43:24.000Z",
  "updated": "2008-06-15T08:29:50.000Z",
  "title": "Weighted Ehrhart Theory and Orbifold Cohomology",
  "authors": [
    "Alan Stapledon"
  ],
  "comment": "23 pages. Final copy, minor changes, to appear in Adv. Math",
  "journal": "Adv. Math. 219 (2008), 63-88.",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "We introduce the notion of a weighted $\\delta$-vector of a lattice polytope. Although the definition is motivated by motivic integration, we study weighted $\\delta$-vectors from a combinatorial perspective. We present a version of Ehrhart Reciprocity and prove a change of variables formula. We deduce a new geometric interpretation of the coefficients of the Ehrhart $\\delta$-vector. More specifically, they are sums of dimensions of orbifold cohomology groups of a toric stack.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2008-06-15T08:29:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20"
    ],
    "keywords": [
      "weighted ehrhart theory",
      "orbifold cohomology groups",
      "toric stack",
      "ehrhart reciprocity",
      "variables formula"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.4382S"
    }
  }
}