{
  "id": "0801.0873",
  "version": "v2",
  "published": "2008-01-06T16:50:40.000Z",
  "updated": "2008-02-23T19:20:39.000Z",
  "title": "Inequalities and Ehrhart $δ$-Vectors",
  "authors": [
    "Alan Stapledon"
  ],
  "comment": "11 pages. v2: minor changes, more detailed proof of Lemma 2.12. To appear in Trans. Amer. Math. Soc",
  "journal": "Trans. Amer. Math. Soc. 361 (2009), 5615-5626.",
  "categories": [
    "math.CO"
  ],
  "abstract": "For any lattice polytope $P$, we consider an associated polynomial $\\bar{\\delta}_{P}(t)$ and describe its decomposition into a sum of two polynomials satisfying certain symmetry conditions. As a consequence, we improve upon known inequalities satisfied by the coefficients of the Ehrhart $\\delta$-vector of a lattice polytope. We also provide combinatorial proofs of two results of Stanley that were previously established using techniques from commutative algebra. Finally, we give a necessary numerical criterion for the existence of a regular unimodular lattice triangulation of the boundary of a lattice polytope.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-02-23T19:20:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20"
    ],
    "keywords": [
      "lattice polytope",
      "inequalities",
      "regular unimodular lattice triangulation",
      "symmetry conditions",
      "combinatorial proofs"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.0873S"
    }
  }
}