{
  "id": "2102.12813",
  "version": "v1",
  "published": "2021-02-25T12:30:04.000Z",
  "updated": "2021-02-25T12:30:04.000Z",
  "title": "A lower bound theorem for $d$-polytopes with $2d+1$ vertices",
  "authors": [
    "Guillermo Pineda-Villavicencio",
    "David Yost"
  ],
  "comment": "26 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We establish the exact lower bound for the number of $k$-faces of $d$-polytopes with $2d+1$ vertices, for each value of $k$, and characterise the minimisers. As a byproduct, we characterise all $d$-polytopes with $d+3$ vertices, and only one or two edges more than the minimum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-25T12:30:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B05"
    ],
    "keywords": [
      "lower bound theorem",
      "exact lower bound",
      "characterise",
      "minimisers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}