{
  "id": "1506.08927",
  "version": "v1",
  "published": "2015-06-30T03:36:24.000Z",
  "updated": "2015-06-30T03:36:24.000Z",
  "title": "Combinatorics of exceptional sequences in type A",
  "authors": [
    "Alexander Garver",
    "Kiyoshi Igusa",
    "Jacob P. Matherne",
    "Jonah Ostroff"
  ],
  "comment": "21 pages. arXiv admin note: substantial text overlap with arXiv:1412.3365",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "Exceptional sequences are certain ordered sequences of quiver representations. We introduce a class of objects called strand diagrams and use this model to classify exceptional sequences of representations of a quiver whose underlying graph is a type $A_n$ Dynkin diagram. We also use variations of this model to classify c-matrices of such quivers, to interpret exceptional sequences as linear extensions of posets, and to give a simple bijection between exceptional sequences and certain chains in the lattice of noncrossing partitions. This work extends a classification of exceptional sequences for the linearly-ordered quiver obtained in an earlier paper by the first and third authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-30T03:36:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "05E10",
      "13F60"
    ],
    "keywords": [
      "combinatorics",
      "interpret exceptional sequences",
      "quiver representations",
      "earlier paper",
      "work extends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150608927G"
    }
  }
}