{
  "id": "2111.07550",
  "version": "v2",
  "published": "2021-11-15T05:59:40.000Z",
  "updated": "2022-12-22T02:44:52.000Z",
  "title": "The $\\mathrm{A}_2$ Andrews-Gordon identities and cylindric partitions",
  "authors": [
    "S. Ole Warnaar"
  ],
  "comment": "46 pages, to appear in Transactions of the AMS, Series B",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP",
    "math.NT",
    "math.RT"
  ],
  "abstract": "Inspired by a number of recent papers by Corteel, Dousse, Foda, Uncu and Welsh on cylindric partitions and Rogers-Ramanujan-type identities, we obtain the $\\mathrm{A}_2$ (or $\\mathrm{A}_2^{(1)}$) analogues of the celebrated Andrews-Gordon identities. We further prove $q$-series identities that correspond to the infinite-level limit of the Andrews-Gordon identities for $\\mathrm{A}_{r-1}$ (or $\\mathrm{A}_{r-1}^{(1)}$) for arbitrary rank $r$. Our results for $\\mathrm{A}_2$ also lead to conjectural, manifestly positive, combinatorial formulas for the $2$-variable generating function of cylindric partitions of rank $3$ and level $d$, such that $d$ is not a multiple of $3$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-12-22T02:44:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A17",
      "05A19",
      "11P84",
      "17B65",
      "33D15"
    ],
    "keywords": [
      "cylindric partitions",
      "combinatorial formulas",
      "arbitrary rank",
      "infinite-level limit",
      "series identities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}