{
  "id": "1905.00570",
  "version": "v1",
  "published": "2019-05-02T04:36:30.000Z",
  "updated": "2019-05-02T04:36:30.000Z",
  "title": "On self-conjugate $(s, s+1,\\ldots, s+k)$-core partitions",
  "authors": [
    "Sherry H. F. Yan",
    "Yao Yu",
    "Hao Zhou"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Simultaneous core partitions have been widely studied since Anderson's work on the enumeration of $(s,t)$-core partitions. Amdeberhan and Leven showed that the number of $(s,s+1, \\ldots, s+k)$-core partitions is equal to the number of $(s, k)$-Dyck paths. In this paper, we prove that self-conjugate $(s,s+1, \\ldots, s+k)$-core partitions are equinumerous with symmetric $(s, k)$-Dyck paths, confirming a conjecture posed by Cho, Huh and Sohn.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-02T04:36:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-conjugate",
      "dyck paths",
      "simultaneous core partitions",
      "andersons work",
      "amdeberhan"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}