{
  "id": "1908.07155",
  "version": "v1",
  "published": "2019-08-20T04:14:28.000Z",
  "updated": "2019-08-20T04:14:28.000Z",
  "title": "Extendable shellability for $d$-dimensional complexes on $d+3$ vertices",
  "authors": [
    "Jared Culbertson",
    "Anton Dochtermann",
    "Dan P. Guralnik",
    "Peter F. Stiller"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO",
    "math.AC",
    "math.GT"
  ],
  "abstract": "We prove that for all $d \\geq 1$ a shellable $d$-dimensional simplicial complex with at most $d+3$ vertices is extendably shellable. The proof involves considering the structure of `exposed' edges in chordal graphs as well as a connection to linear quotients of quadratic monomial ideals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-20T04:14:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "52B22",
      "13D02",
      "13F55"
    ],
    "keywords": [
      "dimensional complexes",
      "extendable shellability",
      "dimensional simplicial complex",
      "quadratic monomial ideals",
      "chordal graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}