{
  "id": "1610.00140",
  "version": "v1",
  "published": "2016-10-01T14:21:06.000Z",
  "updated": "2016-10-01T14:21:06.000Z",
  "title": "Induced bisecting families for hypergraphs",
  "authors": [
    "Niranjan Balachandran",
    "Rogers Mathew",
    "Tapas Kumar Mishra",
    "Sudebkumar Prasant Pal"
  ],
  "comment": "10 pages, 1 fugure",
  "categories": [
    "math.CO"
  ],
  "abstract": "A dot product of two $n$-dimensional vectors $A$ and $B$, $A,B \\in \\mathbb{R}^n$, is said to be \\emph{trivial} if in every coordinate $i \\in [n]$, at least one of $A(i)$ or $B(i)$ is zero. Given the $n$-dimensional Hamming cube $\\{0,1\\}^n$, we study the minimum cardinality of a set $\\mathcal{V}$ of $n$-dimensional $\\{-1,0,1\\}$ vectors, each containing exactly $d$ non-zero entries, such that every point in the Hamming cube has a non-trivial zero dot product with at least one vector $V \\in \\mathcal{V}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-01T14:21:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05C65",
      "G.2.1",
      "G.2.2",
      "F.2.2"
    ],
    "keywords": [
      "induced bisecting families",
      "hypergraphs",
      "non-trivial zero dot product",
      "non-zero entries",
      "dimensional vectors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}