{
  "id": "1412.3365",
  "version": "v1",
  "published": "2014-12-10T16:52:36.000Z",
  "updated": "2014-12-10T16:52:36.000Z",
  "title": "A Combinatorial Model for Exceptional Sequences in Type A",
  "authors": [
    "Alexander Garver",
    "Jacob P. Matherne"
  ],
  "comment": "18 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "Exceptional sequences are certain ordered sequences of quiver representations. We use noncrossing edge-labeled trees in a disk with boundary vertices (expanding on T. Araya's work) to classify exceptional sequences of representations of Q, the linearly-ordered quiver with n vertices. We also show how to use variations of this model to classify c-matrices of Q, to interpret exceptional sequences as linear extensions, and to give a simple bijection between exceptional sequences and certain chains in the lattice of noncrossing partitions. In the case of c-matrices, we also give an interpretation of c-matrix mutation in terms of our noncrossing trees with directed edges.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-10T16:52:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "05E10",
      "13F60"
    ],
    "keywords": [
      "combinatorial model",
      "interpret exceptional sequences",
      "c-matrix mutation",
      "arayas work",
      "classify exceptional sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}