{
  "id": "2302.07118",
  "version": "v1",
  "published": "2023-02-14T15:23:59.000Z",
  "updated": "2023-02-14T15:23:59.000Z",
  "title": "A uniqueness property of τ exceptional sequences",
  "authors": [
    "Eric J. Hanson",
    "Hugh Thomas"
  ],
  "comment": "7 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Recently, Buan and Marsh showed that if two complete $\\tau$-exceptional sequences agree in all but at most one term, then they must agree everywhere, provided the algebra is $\\tau$-tilting finite. They conjectured that the result holds without that assumption. We prove their conjecture. Along the way, we also show that the dimension vectors of the modules in a $\\tau$-exceptional sequence are linearly independent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-14T15:23:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G10"
    ],
    "keywords": [
      "uniqueness property",
      "exceptional sequences agree",
      "result holds",
      "dimension vectors",
      "tilting finite"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}