{
  "id": "2004.08294",
  "version": "v1",
  "published": "2020-04-17T15:09:47.000Z",
  "updated": "2020-04-17T15:09:47.000Z",
  "title": "Dimension of Restricted Classes of Interval Orders",
  "authors": [
    "Mitchel T. Keller",
    "Ann N. Trenk",
    "Stephen J. Young"
  ],
  "comment": "7 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Rabinovitch showed in 1978 that the interval orders having a representation consisting of only closed unit intervals have order dimension at most 3. This article shows that the same dimension bound applies to two other classes of posets: those having a representation consisting of unit intervals (but with a mixture of open and closed intervals allowed) and those having a representation consisting of closed intervals with lengths in $\\{0,1\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-17T15:09:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A07"
    ],
    "keywords": [
      "interval orders",
      "restricted classes",
      "representation consisting",
      "closed intervals",
      "dimension bound applies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}