{
  "id": "1508.00187",
  "version": "v1",
  "published": "2015-08-02T04:15:31.000Z",
  "updated": "2015-08-02T04:15:31.000Z",
  "title": "The numbers of edges of the order polytope and the chain poyltope of a finite partially ordered set",
  "authors": [
    "Takayuki Hibi",
    "Nan Li",
    "Yoshimi Sahara",
    "Akihiro Shikama"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $P$ be an arbitrary finite partially ordered set. It will be proved that the number of edges of the order polytope ${\\mathcal O}(P)$ is equal to that of the chain polytope ${\\mathcal C}(P)$. Furthermore, it will be shown that the degree sequence of the finite simple graph which is the $1$-skeleton of ${\\mathcal O}(P)$ is equal to that of ${\\mathcal C}(P)$ if and only if ${\\mathcal O}(P)$ and ${\\mathcal C}(P)$ are unimodularly equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-02T04:15:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B05",
      "06A07"
    ],
    "keywords": [
      "order polytope",
      "chain poyltope",
      "arbitrary finite partially ordered set",
      "finite simple graph",
      "chain polytope"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150800187H"
    }
  }
}