{
  "id": "2010.06550",
  "version": "v1",
  "published": "2020-10-13T17:03:58.000Z",
  "updated": "2020-10-13T17:03:58.000Z",
  "title": "Connected Chord Diagrams and the Combinatorics of Asymptotic Expansions",
  "authors": [
    "Ali Assem Mahmoud",
    "Karen Yeats"
  ],
  "categories": [
    "math.CO",
    "hep-th"
  ],
  "abstract": "In this article we study an asymptotic expansion for $C_n$, the number of connected chord diagrams on $n$ chords. The expansion is obtained in earlier work by means of alien derivatives applied to the generating series of connected chord diagrams; we seek a combinatorial interpretation. The main outcome presented here is a new combinatorial interpretation for entry \\href{https://oeis.org/A088221}{A088221} of the OEIS. We will show that \\href{https://oeis.org/A088221}{A088221} counts pairs of connected chord diagrams (allowing empty diagrams). This gives a combinatorial interpretation for the part of the closed form of the asymptotic expansion of $C_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-13T17:03:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "connected chord diagrams",
      "asymptotic expansion",
      "combinatorial interpretation",
      "combinatorics",
      "empty diagrams"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}