{
  "id": "1602.04675",
  "version": "v1",
  "published": "2016-02-15T13:54:03.000Z",
  "updated": "2016-02-15T13:54:03.000Z",
  "title": "Intervals of Antichains and Their Decompositions",
  "authors": [
    "Patrick De Causmaecker",
    "Stefan De Wannemacker",
    "Jay Yellen"
  ],
  "comment": "31pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "An antichain of subsets is a set of subsets such that no subset in the antichain is a proper subset of any other subset in the antichain. The Dedekind number counts the total number of antichains of subsets of an n-element set. This paper investigates the interval structure of the lattice of antichains. Several partitioning theorems and counting formulas for the size of intervals are derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-15T13:54:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A07",
      "11B30",
      "05C30",
      "F.2.2",
      "B.2.4",
      "E.1"
    ],
    "keywords": [
      "decompositions",
      "dedekind number counts",
      "interval structure",
      "proper subset",
      "total number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160204675D"
    }
  }
}