{
  "id": "1607.07583",
  "version": "v1",
  "published": "2016-07-26T08:27:40.000Z",
  "updated": "2016-07-26T08:27:40.000Z",
  "title": "Euler's partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identities",
  "authors": [
    "Xinhua Xiong"
  ],
  "comment": "26 pages, submitted to journal",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we give a conjecture, which generalises Euler's partition theorem involving odd parts and different parts for all moduli. We prove this conjecture for two family partitions. We give $q$-difference equations for the related generating function if the moduli is three. We provide new companions to Rogers-Ramanujan-Andrews-Gordon identities under this conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-26T08:27:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P84"
    ],
    "keywords": [
      "rogers-ramanujan-andrews-gordon identities",
      "companions",
      "generalises eulers partition theorem",
      "conjecture",
      "odd parts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}