{
  "id": "1701.08325",
  "version": "v1",
  "published": "2017-01-28T22:08:15.000Z",
  "updated": "2017-01-28T22:08:15.000Z",
  "title": "A new relationship between block designs",
  "authors": [
    "Alexander Shramchenko",
    "Vasilisa Shramchenko"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We propose a procedure of constructing new block designs starting from a given one by looking at the intersections of its blocks with various sets and grouping those sets according to the structure of the intersections. We introduce a symmetric relationship of friendship between block designs built on a set $V$ and consider families of block designs where all designs are friends of each other, the so-called friendly families. We show that a friendly family admits a partial ordering. Furthermore, we exhibit a map from the power set of $V$, partially ordered by inclusion, to a friendly family of a particular type which preserves the partial order.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-28T22:08:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partial order",
      "block designs built",
      "symmetric relationship",
      "power set",
      "intersections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}