{
  "id": "2404.08941",
  "version": "v1",
  "published": "2024-04-13T09:35:33.000Z",
  "updated": "2024-04-13T09:35:33.000Z",
  "title": "A combinatorial approach to Berkovich type identities",
  "authors": [
    "Ji-Cai Liu"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Motivated by Berkovich's nine $q$-binomial identities involving the Legendre symbol $(\\frac{d}{3})$, we establish a unified form of $q$-binomial identities of this type through a combinatorial approach. This unified form includes Berkovich's nine identities as special cases. Many such identities can be also deduced from this unified form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-13T09:35:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "05A10",
      "05A17"
    ],
    "keywords": [
      "berkovich type identities",
      "combinatorial approach",
      "unified form",
      "binomial identities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}