{
  "id": "1210.4029",
  "version": "v1",
  "published": "2012-10-15T13:41:56.000Z",
  "updated": "2012-10-15T13:41:56.000Z",
  "title": "A note on balanced independent sets in the cube",
  "authors": [
    "Ben Barber"
  ],
  "comment": "2 pages",
  "journal": "Australas. J. Combin. 52 (2012), 205-207",
  "categories": [
    "math.CO"
  ],
  "abstract": "Ramras conjectured that the maximum size of an independent set in the discrete cube containing equal numbers of sets of even and odd size is 2^(n-1) - (n-1 choose (n-1)/2) when n is odd. We prove this conjecture, and find the analogous bound when n is even. The result follows from an isoperimetric inequality in the cube.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-15T13:41:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C75"
    ],
    "keywords": [
      "balanced independent sets",
      "discrete cube containing equal numbers",
      "conjecture",
      "isoperimetric inequality"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.4029B"
    }
  }
}