{
  "id": "2311.14997",
  "version": "v1",
  "published": "2023-11-25T11:03:23.000Z",
  "updated": "2023-11-25T11:03:23.000Z",
  "title": "Every latin hypercube of order 5 has transversals",
  "authors": [
    "A. L. Perezhogin",
    "V. N. Potapov",
    "S. Yu. Vladimirov"
  ],
  "comment": "Supplementary data https://zenodo.org/records/10204026",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We prove that for all n>1 every latin n-dimensional cube of order 5 has transversals. We find all 123 paratopy classes of layer-latin cubes of order 5 with no transversals. For each $n\\geq 3$ and $q\\geq 3$ we construct a (2q-2)-layer latin n-dimensional cuboid with no transversals. Moreover, we find all paratopy classes of nonextendible and noncompletable latin cuboids of order 5.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-25T11:03:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B15"
    ],
    "keywords": [
      "latin hypercube",
      "transversals",
      "paratopy classes",
      "latin n-dimensional cube",
      "latin n-dimensional cuboid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}