{
  "id": "1608.08491",
  "version": "v1",
  "published": "2016-08-30T15:09:25.000Z",
  "updated": "2016-08-30T15:09:25.000Z",
  "title": "Fan realizations for some 2-associahedra",
  "authors": [
    "Thibault Manneville"
  ],
  "comment": "24 pages, 17 figures, 7 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "A~$k$-associahedron is a simplicial complex whose facets, called~$k$-triangulations, are the inclusion maximal sets of diagonals of a convex polygon where no~$k+1$ diagonals mutually cross. Such complexes are conjectured for about a decade to have realizations as convex polytopes, and therefore as complete simplicial fans. Apart from four one-parameter families including simplices, cyclic polytopes and classical associahedra, only two instances of multiassociahedra have been geometrically realized so far. This paper reports on conjectural realizations for all~$2$-associahedra, obtained by heuristic methods arising from natural geometric intuition on subword complexes. Experiments certify that we obtain fan realizations of~$2$-associahedra of an~$n$-gon for~$n\\in\\{10,11,12,13\\}$, further ones being out of our computational reach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-30T15:09:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B11",
      "52B12",
      "52B40",
      "05E45"
    ],
    "keywords": [
      "fan realizations",
      "associahedron",
      "inclusion maximal sets",
      "natural geometric intuition",
      "complete simplicial fans"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}