{
  "id": "2401.07492",
  "version": "v1",
  "published": "2024-01-15T06:24:02.000Z",
  "updated": "2024-01-15T06:24:02.000Z",
  "title": "2-levelness of Marked Poset Polytopes",
  "authors": [
    "Jan Stricker"
  ],
  "comment": "19 pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "It is already known that order polytopes and chain polytopes are always 2-level polytopes. In general, this is not true for marked order and marked chain polytopes. We study the geometry of marked order polytopes, marked chain polytopes, and marked chain-order polytopes, providing a comprehensive characterisation of 2-levelness for these polytopes. Furthermore, we present an exact formula for the Ehrhart polynomial of marked order polytopes. Because of their connection to marked chain and marked chain-order polytopes, this polynomial is also the Ehrhart polynomial of these polytopes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-15T06:24:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "52B12",
      "06A07",
      "51M20",
      "05A15"
    ],
    "keywords": [
      "marked poset polytopes",
      "marked chain-order polytopes",
      "marked chain polytopes",
      "marked order polytopes",
      "ehrhart polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}