{
  "id": "2010.07854",
  "version": "v1",
  "published": "2020-10-15T16:21:22.000Z",
  "updated": "2020-10-15T16:21:22.000Z",
  "title": "Limits of Latin squares",
  "authors": [
    "Frederik Garbe",
    "Robert Hancock",
    "Jan Hladký",
    "Maryam Sharifzadeh"
  ],
  "comment": "50 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "We develop a limit theory of Latin squares, paralleling the recent limit theories of dense graphs and permutations. We introduce a notion of density, an appropriate version of the cut distance, and a space of limit objects - so-called Latinons. Key results of our theory are the compactness of the limit space and the equivalence of the topologies induced by the cut distance and the left-convergence. Last, using Keevash's recent results on combinatorial designs, we prove that each Latinon can be approximated by a finite Latin square.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-15T16:21:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B15"
    ],
    "keywords": [
      "limit theory",
      "cut distance",
      "finite latin square",
      "combinatorial designs",
      "appropriate version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}