{
  "id": "1003.1454",
  "version": "v1",
  "published": "2010-03-07T11:27:06.000Z",
  "updated": "2010-03-07T11:27:06.000Z",
  "title": "On the base sequence conjecture",
  "authors": [
    "Dragomir Z. Djokovic"
  ],
  "comment": "19 pages, 10 tables. To appear in Discrete Mathematics.",
  "journal": "Discrete Math. 310 (2010) 1956-1964",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let BS(m,n) denote the set of base sequences (A;B;C;D), with A and B of length m and C and D of length n. The base sequence conjecture (BSC) asserts that BS(n+1,n) exist (i.e., are non-empty) for all n. This is known to be true for n <= 36 and when n is a Golay number. We show that it is also true for n=37 and n=38. It is worth pointing out that BSC is stronger than the famous Hadamard matrix conjecture. In order to demonstrate the abundance of base sequences, we have previously attached to BS(n+1,n) a graph Gamma_n and computed the Gamma_n for n <= 27. We now extend these computations and determine the Gamma_n for n=28,...,35. We also propose a conjecture describing these graphs in general.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-07T11:27:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B20",
      "05B30"
    ],
    "keywords": [
      "base sequence conjecture",
      "famous hadamard matrix conjecture",
      "golay number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.1454D"
    }
  }
}