{
  "id": "2306.16251",
  "version": "v1",
  "published": "2023-06-28T14:25:55.000Z",
  "updated": "2023-06-28T14:25:55.000Z",
  "title": "Companions to the Andrews-Gordon and Andrews-Bressoud identities, and recent conjectures of Capparelli, Meurman, Primc, and Primc",
  "authors": [
    "Matthew C. Russell"
  ],
  "categories": [
    "math.CO",
    "math.NT",
    "math.RT"
  ],
  "abstract": "We find bivariate generating functions for the $k=1$ cases of recently conjectured colored partition identities of Capparelli, Meurman, A. Primc, and M. Primc that are slight variants of the generating functions for the sum sides of the Andrews-Gordon and Andrews-Bressoud identities. As a consequence, we prove sum-to-product identities for these cases, thus proving the conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-28T14:25:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P84",
      "05A17",
      "17B67"
    ],
    "keywords": [
      "andrews-bressoud identities",
      "conjectures",
      "capparelli",
      "andrews-gordon",
      "companions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}