{
  "id": "2406.15614",
  "version": "v1",
  "published": "2024-06-21T19:29:46.000Z",
  "updated": "2024-06-21T19:29:46.000Z",
  "title": "Duplicated Steiner triple systems with self-orthogonal near resolutions",
  "authors": [
    "Peter J. Dukes",
    "Esther R. Lamken"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A Steiner triple system, STS$(v)$, is a family of $3$-subsets (blocks) of a set of $v$ elements such that any two elements occur together in precisely one block. A collection of triples consisting of two copies of each block of an STS is called a duplicated Steiner triple system, DSTS. A resolvable (or near resolvable) DSTS is called self-orthogonal if every pair of distinct classes in the resolution has at most one block in common. We provide several methods to construct self-orthogonal near resolvable DSTS and settle the existence of such designs for all values of $v$ with only four possible exceptions. This addresses a recent question of Bryant, Davies and Neubecker.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-21T19:29:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B07",
      "05B15"
    ],
    "keywords": [
      "duplicated steiner triple system",
      "resolution",
      "elements occur",
      "distinct classes",
      "construct self-orthogonal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}