{
  "id": "2402.15886",
  "version": "v2",
  "published": "2024-02-24T19:34:15.000Z",
  "updated": "2024-03-18T23:11:52.000Z",
  "title": "Extension of Bressoud's generalization of Borwein's conjecture and some exact results",
  "authors": [
    "Alexander Berkovich",
    "Aritram Dhar"
  ],
  "comment": "13 pages, 2 figures. Comments are welcome!",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "In this paper, we conjecture an extension to Bressoud's 1996 generalization of Borwein's famous 1990 conjecture. We then state three infinite hierarchies of non-negative $q$-series identities which are interesting examples of our proposed conjecture and Bressoud's generalized conjecture. Finally, using certain positivity-preserving transformations for $q$-binomial coefficients, we prove the non-negativity of the three infinite families.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-03-18T23:11:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A17",
      "05A30",
      "11P81",
      "11P84"
    ],
    "keywords": [
      "borweins conjecture",
      "exact results",
      "bressouds generalization",
      "infinite hierarchies",
      "series identities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}