{
  "id": "1906.04719",
  "version": "v1",
  "published": "2019-06-11T17:45:55.000Z",
  "updated": "2019-06-11T17:45:55.000Z",
  "title": "The $h^*$-polynomials of locally anti-blocking lattice polytopes and their $γ$-positivity",
  "authors": [
    "Hidefumi Ohsugi",
    "Akiyoshi Tsuchiya"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A lattice polytope $\\mathcal{P} \\subset \\mathbb{R}^d$ is called a locally anti-blocking polytope if for any closed orthant $\\mathbb{R}^d_{\\varepsilon}$ in $\\mathbb{R}^d$, $\\mathcal{P} \\cap \\mathbb{R}^d_{\\varepsilon}$ is unimodularly equivalent to an anti-blocking polytope by reflections of coordinate hyperplanes. In the present paper, we give a formula of the $h^*$-polynomials of locally anti-blocking lattice polytopes. In particular, we discuss the $\\gamma$-positivity of the $h^*$-polynomials of locally anti-blocking reflexive polytopes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-11T17:45:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05C31",
      "13P10",
      "52B12",
      "52B20"
    ],
    "keywords": [
      "locally anti-blocking lattice polytopes",
      "polynomials",
      "positivity",
      "coordinate hyperplanes",
      "locally anti-blocking polytope"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}