{
  "id": "2311.04409",
  "version": "v1",
  "published": "2023-11-08T00:29:29.000Z",
  "updated": "2023-11-08T00:29:29.000Z",
  "title": "Signed Poset Polytopes",
  "authors": [
    "Matthias Beck",
    "Max Hlavacek"
  ],
  "comment": "17 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Stanley introduced in 1986 the order polytope and the chain polytope for a given finite poset. These polytopes contain much information about the poset and have given rise to important examples in polyhedral geometry. In 1993, Reiner introduced signed posets as natural type-B analogues of posets. We define and study signed order and chain polytopes. Our results include convex-hull and halfspace descriptions, unimodular triangulations, Ehrhart $h^*$-polynomials and their relations to signed permutation statistics, and a Gorenstein characterization of signed order and chain polytopes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-08T00:29:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "05A15",
      "05C22",
      "52C07"
    ],
    "keywords": [
      "signed poset polytopes",
      "chain polytope",
      "natural type-b analogues",
      "important examples",
      "order polytope"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}