{
  "id": "math/0601463",
  "version": "v2",
  "published": "2006-01-19T10:02:27.000Z",
  "updated": "2006-12-22T05:52:58.000Z",
  "title": "Overpartitions, lattice paths and Rogers-Ramanujan identities",
  "authors": [
    "Sylvie Corteel",
    "Olivier Mallet"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We extend partition-theoretic work of Andrews, Bressoud, and Burge to overpartitions, defining the notions of successive ranks, generalized Durfee squares, and generalized lattice paths, and then relating these to overpartitions defined by multiplicity conditions on the parts. This leads to many new partition and overpartition identities, and provides a unification of a number of well-known identities of the Rogers-Ramanujan type. Among these are Gordon's generalization of the Rogers-Ramanujan identities, Andrews' generalization of the G\\\"ollnitz-Gordon identities, and Lovejoy's ``Gordon's theorems for overpartitions.\"",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-12-22T05:52:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P81",
      "05A17"
    ],
    "keywords": [
      "rogers-ramanujan identities",
      "extend partition-theoretic work",
      "generalized durfee squares",
      "generalized lattice paths",
      "multiplicity conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1463C"
    }
  }
}