{
  "id": "2104.04338",
  "version": "v1",
  "published": "2021-04-09T12:51:34.000Z",
  "updated": "2021-04-09T12:51:34.000Z",
  "title": "Two proofs of the $q,t$-symmetry of the generalized $q,t$-Catalan number $C_{(k_1,k_2,k_3)}(q,t)$",
  "authors": [
    "Guoce Xin",
    "Yingrui Zhang"
  ],
  "comment": "13 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give two proofs of the $q,t$-symmetry of the generalized $q,t$-Catalan number $C_{\\vec{k}}(q,t)$ for $\\vec{k}=(k_1,k_2,k_3)$. One is by MacMahon's partition analysis as we proposed; the other is by a direct bijection.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-09T12:51:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "catalan number",
      "macmahons partition analysis",
      "direct bijection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}