{
  "id": "1106.3013",
  "version": "v1",
  "published": "2011-06-15T16:10:46.000Z",
  "updated": "2011-06-15T16:10:46.000Z",
  "title": "Combinatorial Telescoping for an Identity of Andrews on Parity in Partitions",
  "authors": [
    "William Y. C. Chen",
    "Daniel K. Du",
    "Charles B. Mei"
  ],
  "comment": "12 pages, 5 figures",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Following the method of combinatorial telescoping for alternating sums given by Chen, Hou and Mu, we present a combinatorial telescoping approach to partition identities on sums of positive terms. By giving a classification of the combinatorial objects corresponding to a sum of positive terms, we establish bijections that lead a telescoping relation. We illustrate this idea by giving a combinatorial telescoping relation for a classical identity of MacMahon. Recently, Andrews posed a problem of finding a combinatorial proof of an identity on the q-little Jacobi polynomials which was derived based on a recurrence relation. We find a combinatorial classification of certain triples of partitions and a sequence of bijections. By the method of cancelation, we see that there exists an involution for a recurrence relation that implies the identity of Andrews.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-15T16:10:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P83"
    ],
    "keywords": [
      "recurrence relation",
      "positive terms",
      "q-little jacobi polynomials",
      "combinatorial classification",
      "partition identities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.3013C"
    }
  }
}