{
  "id": "1304.0949",
  "version": "v3",
  "published": "2013-04-03T13:30:41.000Z",
  "updated": "2014-03-27T14:06:19.000Z",
  "title": "Extremal set theory, cubic forms on $\\mathbb{F}_2^n$ and Hurwitz square identities",
  "authors": [
    "Sophie Morier-Genoud",
    "Valentin Ovsienko"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We consider a family, $\\mathcal{F}$, of subsets of an $n$-set such that the cardinality of the symmetric difference of any two elements $F,F'\\in\\mathcal{F}$ is not a multiple of 4. We prove that the maximal size of $\\mathcal{F}$ is bounded by $2n$, unless $n\\equiv{}3\\mod4$ when it is bounded by $2n+2$. Our method uses cubic forms on $\\mathbb{F}_2^n$ and the Hurwitz-Radon theory of square identities. We also apply this theory to obtain some information about boolean cubic forms and so-called additive quadruples.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-27T14:06:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "11B30",
      "11E25",
      "17A99"
    ],
    "keywords": [
      "extremal set theory",
      "hurwitz square identities",
      "boolean cubic forms",
      "symmetric difference",
      "hurwitz-radon theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.0949M"
    }
  }
}