{
  "id": "1906.00366",
  "version": "v1",
  "published": "2019-06-02T08:54:48.000Z",
  "updated": "2019-06-02T08:54:48.000Z",
  "title": "Partition function of the cyclic group",
  "authors": [
    "Steven S Poon"
  ],
  "comment": "15 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper addresses the problem of finding $Q_{m,t}\\left(n\\right)$, the number of possible ways to partition any member $n$ of the cyclic group $\\mathbb{Z}/m\\mathbb{Z}$ into $t$ distinct parts. When $m$ is odd, it was previously known that the number of partitions of the identity element $0\\bmod m$ with distinct parts is equal to the number of possible bi-color necklaces with $m$ beads. This paper will expand upon this result by showing the equivalence between $Q_{m,t}\\left(n\\right)$ and the number of bi-color necklaces meeting certain periodicity requirements, even when $m$ is even.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-02T08:54:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclic group",
      "partition function",
      "distinct parts",
      "bi-color necklaces",
      "paper addresses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}