{
  "id": "1303.4336",
  "version": "v1",
  "published": "2013-03-18T17:44:08.000Z",
  "updated": "2013-03-18T17:44:08.000Z",
  "title": "Supersaturation in the Boolean lattice",
  "authors": [
    "Andrew P. Dove",
    "Jerrold R. Griggs",
    "Ross J. Kang",
    "Jean-Sébastien Sereni"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We prove a \"supersaturation-type\" extension of both Sperner's Theorem (1928) and its generalization by Erdos (1945) to k-chains. Our result implies that a largest family whose size is x more than the size of a largest k-chain free family and that contains the minimum number of k-chains is the family formed by taking the middle (k-1) rows of the Boolean lattice and x elements from the k-th middle row. We prove our result using the symmetric chain decomposition method of de Bruijn, van Ebbenhorst Tengbergen, and Kruyswijk (1951).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-18T17:44:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boolean lattice",
      "supersaturation",
      "symmetric chain decomposition method",
      "k-th middle row",
      "van ebbenhorst tengbergen"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.4336D"
    }
  }
}