{
  "id": "2404.16215",
  "version": "v1",
  "published": "2024-04-24T21:29:35.000Z",
  "updated": "2024-04-24T21:29:35.000Z",
  "title": "An Overpartition Companion of Andrews and Keith's 2-colored $q$-series Identity",
  "authors": [
    "Hunter Waldron"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Andrews and Keith recently produced a general Schmidt type partition theorem using a novel interpretation of Stockhofe's bijection, which they used to find new $q$-series identities. This includes an identity for a trivariate 2-colored partition generating function. In this paper, their Schmidt type theorem is further generalized akin to how Franklin classically extended Glaisher's theorem. As a consequence, we obtain a companion to Andrews and Keith's 2-colored identity for overpartitions. These identities appear to be special cases of a much more general result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-24T21:29:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "series identity",
      "overpartition companion",
      "general schmidt type partition theorem",
      "franklin classically extended glaishers theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}