{
  "id": "1708.03250",
  "version": "v1",
  "published": "2017-08-10T15:06:43.000Z",
  "updated": "2017-08-10T15:06:43.000Z",
  "title": "The mixed degree of families of lattice polytopes",
  "authors": [
    "Benjamin Nill"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The degree of a lattice polytope is a notion in Ehrhart theory that was studied quite intensively over the previous years. It is well-known that a lattice polytope has normalized volume one if and only if its degree is zero. Recently, Esterov and Gusev gave a complete classification result of families of $n$ lattice polytopes in $\\mathbb{R}^n$ whose mixed volume equals one. Here, we give a reformulation of their result involving the novel notion of a mixed degree that generalizes the degree similar to how the mixed volume generalizes the volume. We discuss and motivate this terminology, and explain why it extends a previous definition of Soprunov. We also remark how a recent combinatorial result due to Bihan solves a related problem posed by Soprunov.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-10T15:06:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "52A39"
    ],
    "keywords": [
      "lattice polytope",
      "mixed degree",
      "complete classification result",
      "combinatorial result",
      "ehrhart theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}