{
  "id": "2006.03878",
  "version": "v1",
  "published": "2020-06-06T14:36:49.000Z",
  "updated": "2020-06-06T14:36:49.000Z",
  "title": "Tiling proofs of Jacobi triple product and Rogers-Ramanujan identities",
  "authors": [
    "Alok Shukla"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We use the method of tiling to give elementary combinatorial proofs of some celebrated $q$-series identities, such as Jacobi triple product identity and Rogers-Ramanujan identities. A new generalized $ k $-product $q$-series identity is also obtained by employing the tiling-method, wherein the generating function of the set of all possible tilings of a rectangular board is computed in two different ways to obtain the desired $q$-series identity. The tiling-method holds promise for giving an aesthetically pleasing approach to prove old and new $q$-series identities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-06T14:36:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P84",
      "05A17",
      "05A19",
      "11P81"
    ],
    "keywords": [
      "rogers-ramanujan identities",
      "series identity",
      "tiling proofs",
      "jacobi triple product identity",
      "tiling-method holds promise"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}