{
  "id": "2110.00544",
  "version": "v2",
  "published": "2021-10-01T17:16:22.000Z",
  "updated": "2025-05-09T15:46:40.000Z",
  "title": "Associahedra minimize $f$-vectors of secondary polytopes of planar point sets",
  "authors": [
    "Antonio Fernández",
    "Francisco Santos"
  ],
  "comment": "23 pages, 6 figures. Main changes from previous version are an extended introduction, now spit in two sections, \"Introduction\" and \"Preliminaries on regular subdivisions\"",
  "journal": "Discrete Comput Geom, published online 9 May 2025",
  "doi": "10.1007/s00454-025-00738-1",
  "categories": [
    "math.CO"
  ],
  "abstract": "Kupavskii, Volostnov, and Yarovikov have recently shown that any set of $n$ points in general position in the plane has at least as many (partial) triangulations as the convex $n$-gon. We generalize this in two directions: we show that regular triangulations are enough, and we extend the result to all regular subdivisions, graded by the dimension of their corresponding face in the secondary polytope.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-05-09T15:46:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C20",
      "52B05",
      "05C30"
    ],
    "keywords": [
      "planar point sets",
      "secondary polytope",
      "associahedra minimize",
      "general position",
      "regular triangulations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}