{
  "id": "1110.3724",
  "version": "v1",
  "published": "2011-10-17T16:35:11.000Z",
  "updated": "2011-10-17T16:35:11.000Z",
  "title": "Unimodality questions for integrally closed lattice polytopes",
  "authors": [
    "Jan Schepers",
    "Leen Van Langenhoven"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "It is a famous open question whether every integrally closed reflexive polytope has a unimodal Ehrhart delta-vector. We generalize this question to arbitrary integrally closed lattice polytopes and we prove unimodality for the delta-vector of lattice parallelepipeds. This is the first nontrivial class of integrally closed polytopes. Moreover, we suggest a new approach to the problem for reflexive polytopes via triangulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-17T16:35:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "05A20",
      "11B68"
    ],
    "keywords": [
      "unimodality questions",
      "reflexive polytope",
      "arbitrary integrally closed lattice polytopes",
      "first nontrivial class",
      "unimodal ehrhart delta-vector"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.3724S"
    }
  }
}