{
  "id": "1803.02515",
  "version": "v1",
  "published": "2018-03-07T03:22:53.000Z",
  "updated": "2018-03-07T03:22:53.000Z",
  "title": "Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type",
  "authors": [
    "Shashank Kanade",
    "Matthew C. Russell"
  ],
  "categories": [
    "math.CO",
    "math.NT",
    "math.QA",
    "math.RT"
  ],
  "abstract": "We utilize the technique of staircases and jagged partitions to provide analytic sum-sides to some old and new partition identities of Rogers-Ramanujan type. Firstly, we conjecture a class of new partition identities related to the principally specialized characters of certain level $2$ modules for the affine Lie algebra $A_9^{(2)}$. Secondly, we provide analytic sum-sides to some earlier conjectures of the authors. Next, we use these analytic sum-sides to discover a number of further generalizations. Lastly, we apply this technique to the well-known Capparelli identities and present analytic sum-sides which we believe to be new. All of the new conjectures presented in this article are supported by a strong mathematical evidence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-07T03:22:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A17",
      "11P84",
      "17B69"
    ],
    "keywords": [
      "analytic sum-sides",
      "integer partition identities",
      "rogers-ramanujan type",
      "staircases",
      "affine lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}