{
  "id": "1908.06679",
  "version": "v1",
  "published": "2019-08-19T10:09:56.000Z",
  "updated": "2019-08-19T10:09:56.000Z",
  "title": "The 3-way flower intersection problem for Steiner triple systems",
  "authors": [
    "H. Amjadi",
    "N. Soltankhah"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The flower at a point x in a Steiner triple system (X; B) is the set of all triples containing x. Denote by J3F(r) the set of all integers k such that there exists a collection of three STS(2r+1) mutually intersecting in the same set of k + r triples, r of them being the triples of a common flower. In this article we determine the set J3F(r) for any positive integer r = 0, 1 (mod 3) (only some cases are left undecided for r = 6, 7, 9, 24), and establish that J3F(r) = I3F(r) for r = 0, 1 (mod 3) where I3F(r) = {0, 1,..., 2r(r-1)/3-8, 2r(r-1)/3-6, 2r(r-1)/3}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-19T10:09:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B05"
    ],
    "keywords": [
      "steiner triple system",
      "flower intersection problem",
      "common flower",
      "set j3f",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}