{
  "id": "1905.00613",
  "version": "v1",
  "published": "2019-05-02T08:22:34.000Z",
  "updated": "2019-05-02T08:22:34.000Z",
  "title": "Combinatorics of faithfully balanced modules",
  "authors": [
    "William Crawley-Boevey",
    "Biao Ma",
    "Baptiste Rognerud",
    "Julia Sauter"
  ],
  "comment": "28 pages, 5 figures",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We study and classify faithfully balanced modules for the algebra of lower triangular $n$ by $n$ matrices. The theory extends known results about tilting modules, which are classified by binary trees, and counted with the Catalan numbers. The number of faithfully balanced modules is a $2$-factorial number. Among them are $n!$ modules with $n$ indecomposable summands, which can be classified by interleaved binary trees or by increasing binary trees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-02T08:22:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10"
    ],
    "keywords": [
      "combinatorics",
      "lower triangular",
      "interleaved binary trees",
      "factorial number",
      "increasing binary trees"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}