{
  "id": "1208.1805",
  "version": "v6",
  "published": "2012-08-09T02:51:55.000Z",
  "updated": "2013-04-14T10:57:11.000Z",
  "title": "General lower bounds on maximal determinants of binary matrices",
  "authors": [
    "Richard P. Brent",
    "Judy-anne H. Osborn"
  ],
  "comment": "15 pages, 37 references, 1 table. Typos corrected and theorems renumbered in v6",
  "journal": "The Electronic Journal of Combinatorics 20(2), 2013, #P15",
  "categories": [
    "math.CO",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We give general lower bounds on the maximal determinant of n by n {+1,-1}-matrices, both with and without the assumption of the Hadamard conjecture. Our bounds improve on earlier results of de Launey and Levin (2010) and, for certain congruence classes of n mod 4, those of Koukouvinos, Mitrouli and Seberry (2000). In an Appendix we give a new proof, using Jacobi's determinant identity, of a result of Sz\\\"oll\\H{o}si (2010) on minors of Hadamard matrices.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2013-04-14T10:57:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B20",
      "15A15",
      "15B34",
      "62K05"
    ],
    "keywords": [
      "general lower bounds",
      "maximal determinant",
      "binary matrices",
      "jacobis determinant identity",
      "hadamard conjecture"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1805B"
    }
  }
}