{
  "id": "1909.05887",
  "version": "v1",
  "published": "2019-09-12T18:04:43.000Z",
  "updated": "2019-09-12T18:04:43.000Z",
  "title": "Exceptional Sequences and Idempotent Functions",
  "authors": [
    "Emre Sen"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.RT"
  ],
  "abstract": "We prove that there is one to one correspondence between the following three: idempotent functions on the set of size $n$, exceptional sequences of linear radical square zero Nakayama algebras of rank $n$ and rooted labeled forests with $n$ nodes and height of at most one. Therefore, the number of exceptional sequences is given by the sum $\\sum\\limits^n_{j=1}\\binom{n}{j}j^{n-j}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-12T18:04:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "05E10",
      "05C30"
    ],
    "keywords": [
      "exceptional sequences",
      "idempotent functions",
      "linear radical square zero nakayama",
      "radical square zero nakayama algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}