{
  "id": "1503.01643",
  "version": "v1",
  "published": "2015-03-05T14:28:00.000Z",
  "updated": "2015-03-05T14:28:00.000Z",
  "title": "Mosaics of Combinatorial Designs",
  "authors": [
    "Oliver W. Gnilke",
    "Marcus Greferath",
    "Mario Osvin Pavčević"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "Looking at incidence matrices of $t$-$(v,k,\\lambda)$ designs as $v \\times b$ matrices with $2$ possible entries, each of which indicates incidences of a $t$-design, we introduce the notion of a $c$-mosaic of designs, having the same number of points and blocks, as a matrix with $c$ different entries, such that each entry defines incidences of a design. In fact, a $v \\times b$ matrix is decomposed in $c$ incidence matrices of designs, each denoted by a different colour, hence this decomposition might be seen as a tiling of a matrix with incidence matrices of designs as well. These mosaics have applications in experiment design when considering a simultaneous run of several different experiments. We have constructed infinite series of examples of mosaics and state some probably non-trivial open problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-05T14:28:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B30",
      "05B05"
    ],
    "keywords": [
      "combinatorial designs",
      "incidence matrices",
      "entry defines incidences",
      "probably non-trivial open problems",
      "experiment design"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150301643G"
    }
  }
}