{
  "id": "1809.07866",
  "version": "v1",
  "published": "2018-09-20T21:11:57.000Z",
  "updated": "2018-09-20T21:11:57.000Z",
  "title": "Constructions and uses of incomplete pairwise balanced designs",
  "authors": [
    "Peter J. Dukes",
    "Esther R. Lamken"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We give explicit constructions for incomplete pairwise balanced designs IPBD$((v;w),K)$, or, equivalently, edge-decompositions of a difference of two cliques $K_v \\setminus K_w$ into cliques whose sizes belong to the set $K$. Our constructions produce such designs whenever $v$ and $w$ satisfy the usual divisibility conditions, have ratio $v/w$ bounded away from the smallest value in $K$ minus one, say $v/w > k-1+\\epsilon$, for $k =\\min K$ and $\\epsilon>0$, and are sufficiently large (depending on $K$ and $\\epsilon$). As a consequence, some new results are obtained on many related designs, including class-uniformly resolvable designs, incomplete mutually orthogonal latin squares, and group divisible designs. We also include several other applications that illustrate the power of using IPBDs as `templates'.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-20T21:11:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B05",
      "05B15",
      "05C70"
    ],
    "keywords": [
      "constructions",
      "incomplete mutually orthogonal latin squares",
      "usual divisibility conditions",
      "incomplete pairwise balanced designs ipbd",
      "sizes belong"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}