{
  "id": "2012.14380",
  "version": "v1",
  "published": "2020-12-28T17:41:02.000Z",
  "updated": "2020-12-28T17:41:02.000Z",
  "title": "A complete characterization of $(f_0, f_1)$-pairs of 6-polytopes",
  "authors": [
    "Karim Adiprasito",
    "Rémi Cocou Avohou"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We completely characterize the first two entries, namely the $(f_0, f_1)$-vector pairs, for $6$-dimension polytopes. We also find the characterization for $7$-dimension polytopes with excess degree greater than $11$ and, we conjecture bounds fulfilled by $(f_0, f_1)$-vector pairs for any $d$-polytope having an excess degree greater than $3d-10$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-28T17:41:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "57M15"
    ],
    "keywords": [
      "complete characterization",
      "excess degree greater",
      "vector pairs",
      "dimension polytopes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}