{
  "id": "2404.00263",
  "version": "v1",
  "published": "2024-03-30T06:37:01.000Z",
  "updated": "2024-03-30T06:37:01.000Z",
  "title": "Triangular faces of the order and chain polytope of a maximal ranked poset",
  "authors": [
    "Aki Mori"
  ],
  "comment": "7 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathscr{O}(P)$ and $\\mathscr{C}(P)$ denote the order polytope and chain polytope, respectively, associated with a finite poset $P$. We prove the following result: if $P$ is a maximal ranked poset, then the number of triangular $2$-faces of $\\mathscr{O}(P)$ is less than or equal to that of $\\mathscr{C}(P)$, with equality holding if and only if $P$ does not contain an $X$-poset as a subposet.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-30T06:37:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B05",
      "06A07"
    ],
    "keywords": [
      "maximal ranked poset",
      "chain polytope",
      "triangular faces",
      "order polytope",
      "finite poset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}