{
  "id": "2306.09072",
  "version": "v1",
  "published": "2023-06-15T12:04:37.000Z",
  "updated": "2023-06-15T12:04:37.000Z",
  "title": "Decomposition of an Integrally Convex Set into a Minkowski Sum of Bounded and Conic Integrally Convex Sets",
  "authors": [
    "Kazuo Murota",
    "Akihisa Tamura"
  ],
  "comment": "23 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of discrete sets in discrete convex analysis, such as integrally convex sets, L-natural-convex sets, and M-natural-convex sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-15T12:04:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A41",
      "90C27",
      "90C25"
    ],
    "keywords": [
      "conic integrally convex sets",
      "minkowski sum",
      "paper establishes similar statements",
      "decomposition",
      "discrete convex analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}