{
  "id": "2010.13996",
  "version": "v1",
  "published": "2020-10-27T02:14:06.000Z",
  "updated": "2020-10-27T02:14:06.000Z",
  "title": "Lengths of maximal green sequences for tame path algebras",
  "authors": [
    "Ryoichi Kase",
    "Ken Nakashima"
  ],
  "comment": "67 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "In this paper, we study the maximal length of maximal green sequences for quivers of type $\\widetilde{\\mathbf{D}}$ and $\\widetilde{\\mathbf{E}}$ by using the theory of tilting mutation. We show that the maximal length does not depend on the choice of the orientation, and determine it explicitly. Moreover, we give a program which counts all maximal green sequences by length for a given Dynkin/extended Dynkin quiver.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-27T02:14:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "06-08",
      "16G60"
    ],
    "keywords": [
      "maximal green sequences",
      "tame path algebras",
      "maximal length",
      "dynkin/extended dynkin quiver",
      "orientation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 67,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}