{
  "id": "1707.07573",
  "version": "v1",
  "published": "2017-07-24T14:31:19.000Z",
  "updated": "2017-07-24T14:31:19.000Z",
  "title": "A note on the van der Waerden complex",
  "authors": [
    "Becky Hooper",
    "Adam Van Tuyl"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "Ehrenborg, Govindaiah, Park, and Readdy recently introduced the van der Waerden complex, a pure simplicial complex whose facets correspond to arithmetic progressions. Using techniques from combinatorial commutative algebra, we classify when these pure simplicial complexes are vertex decomposable or not Cohen-Macaulay. As a corollary, we classify the van der Waerden complexes that are shellable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-24T14:31:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "13F55"
    ],
    "keywords": [
      "van der waerden complex",
      "pure simplicial complex",
      "arithmetic progressions",
      "facets correspond",
      "combinatorial commutative algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}