{
  "id": "1301.4764",
  "version": "v1",
  "published": "2013-01-21T06:36:46.000Z",
  "updated": "2013-01-21T06:36:46.000Z",
  "title": "The 3-way intersection problem for S(2, 4, v) designs",
  "authors": [
    "Saeedeh Rashidi",
    "Nasrin Soltankhah"
  ],
  "comment": "accepted in Utilitas mathematics",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper the 3-way intersection problem for $S(2,4,v)$ designs is investigated. Let $b_{v}=\\frac {v(v-1)}{12}$ and $I_{3}[v]=\\{0,1,...,b_{v}\\}\\setminus\\{b_{v}-7,b_{v}-6,b_{v}-5,b_{v}-4,b_{v}-3,b_{v}-2,b_{v}-1\\}$. Let $J_{3}[v]=\\{k|$ there exist three $S(2,4,v)$ designs with $k$ same common blocks$\\}$. We show that $J_{3}[v]\\subseteq I_{3}[v]$ for any positive integer $v\\equiv1, 4\\ (\\rm mod \\ 12)$ and $J_{3}[v]=I_{3}[v]$, for $ v\\geq49$ and $v=13 $. We find $J_{3}[16]$ completely. Also we determine some values of $J_{3}[v]$ for $\\ v=25,28,37$ and 40.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-21T06:36:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "intersection problem",
      "common blocks",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.4764R"
    }
  }
}