{
  "id": "1608.03635",
  "version": "v1",
  "published": "2016-08-11T23:33:44.000Z",
  "updated": "2016-08-11T23:33:44.000Z",
  "title": "Proof of Xiong's conjectured refinement of Euler's partition theorem",
  "authors": [
    "William J. Keith"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In a recent preprint, Xinhua Xiong conjectured a refinement of Euler's partition theorem that partitions with distinct parts are equinumerous with those into odd parts. His conjecture applies to all moduli and generalizes a result of Pak and Postnikov on partitions with all parts having the same residue with respect to a given modulus. This note bijectively proves Xiong's conjecture in its full generality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-11T23:33:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P81",
      "11P83"
    ],
    "keywords": [
      "eulers partition theorem",
      "xiongs conjectured refinement",
      "distinct parts",
      "xinhua xiong",
      "odd parts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}