{
  "id": "1207.3206",
  "version": "v1",
  "published": "2012-07-13T11:42:25.000Z",
  "updated": "2012-07-13T11:42:25.000Z",
  "title": "Torsion pairs in cluster tubes",
  "authors": [
    "Thorsten Holm",
    "Peter Jorgensen",
    "Martin Rubey"
  ],
  "comment": "19 pages",
  "journal": "Journal of Algebraic Combinatorics 39 (2014), 587-605",
  "doi": "10.1007/s10801-013-0457-6",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We give a complete classification of torsion pairs in the cluster categories associated to tubes of finite rank. The classification is in terms of combinatorial objects called Ptolemy diagrams which already appeared in our earlier work on torsion pairs in cluster categories of Dynkin type A. As a consequence of our classification we establish closed formulae enumerating the torsion pairs in cluster tubes, and obtain that the torsion pairs in cluster tubes exhibit a cyclic sieving phenomenon.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-13T11:42:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G70",
      "05E15",
      "13F60",
      "18E30"
    ],
    "keywords": [
      "torsion pairs",
      "cluster tubes",
      "cyclic sieving phenomenon",
      "finite rank",
      "combinatorial objects"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.3206H"
    }
  }
}