{
  "id": "2403.07217",
  "version": "v1",
  "published": "2024-03-12T00:14:49.000Z",
  "updated": "2024-03-12T00:14:49.000Z",
  "title": "Arrow Relations in Lattices of Integer Partitions",
  "authors": [
    "Asma'a Almazaydeh",
    "Mike Behrisch",
    "Edith Vargas-García",
    "Andreas Wachtel"
  ],
  "comment": "28 pages, 8 figures, 3 tables and 3 contexts",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We give a complete characterisation of the single and double arrow relations of the standard context $K(L_n)$ of the lattice $L_n$ of partitions of any positive integer $n$ under the dominance order, thereby addressing an open question of Ganter, 2022.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-12T00:14:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P81",
      "06B23",
      "06A07",
      "06B05",
      "06B15"
    ],
    "keywords": [
      "integer partitions",
      "complete characterisation",
      "standard context",
      "open question",
      "dominance order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}