{
  "id": "1403.5378",
  "version": "v3",
  "published": "2014-03-21T06:39:41.000Z",
  "updated": "2014-08-27T19:25:22.000Z",
  "title": "Ehrhart series, unimodality, and integrally closed reflexive polytopes",
  "authors": [
    "Benjamin Braun",
    "Robert Davis"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "An interesting open problem in Ehrhart theory is to classify those lattice polytopes having a unimodal $h^*$-vector. Although various sufficient conditions have been found, necessary conditions remain a challenge. In this paper, we consider integrally closed reflexive simplices and discuss an operation that preserves reflexivity, integral closure, and unimodality of the $h^*$-vector, providing one explanation for why unimodality occurs in this setting. We also discuss the failure of proving unimodality in this setting using weak Lefschetz elements.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-25T17:08:55.000Z",
      "abstract": "An interesting open problem in Ehrhart theory is to classify those lattice polytopes having a unimodal $h^*$-vector. Although various sufficient conditions have been found, necessary conditions remain a challenge. In this paper, we consider integrally closed reflexive polytopes and discuss an operation that preserves reflexivity, integral closure, and unimodality of the $h^*$-vector, providing one explanation for why unimodality occurs in this setting. We also discuss the special case of reflexive simplices.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-08-27T19:25:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "52B20"
    ],
    "keywords": [
      "integrally closed reflexive polytopes",
      "ehrhart series",
      "unimodality",
      "necessary conditions remain",
      "ehrhart theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.5378B"
    }
  }
}