{
  "id": "1704.01666",
  "version": "v1",
  "published": "2017-04-05T23:14:11.000Z",
  "updated": "2017-04-05T23:14:11.000Z",
  "title": "Optimal transport and integer partitions",
  "authors": [
    "Sonja Hohloch"
  ],
  "comment": "21 pages, 7 figures; In accordance with the journal's copyright, I am making a preprint version of my published paper available on the ArXiv",
  "journal": "Discrete Applied Mathematics 190/191 (2015), 75 - 85",
  "categories": [
    "math.NT",
    "math.CO",
    "math.OC"
  ],
  "abstract": "We link the theory of optimal transportation to the theory of integer partitions. Let $\\mathscr P(n)$ denote the set of integer partitions of $n \\in \\mathbb N$ and write partitions $\\pi \\in \\mathscr P(n)$ as $(n_1, \\dots, n_{k(\\pi)})$. Using terminology from optimal transport, we characterize certain classes of partitions like symmetric partitions and those in Euler's identity $|\\{ \\pi \\in \\mathscr P(n) |$ all $ n_i $ distinct $ \\} | = | \\{ \\pi \\in \\mathscr P(n) | $ all $ n_i $ odd $ \\}|$. Then we sketch how optimal transport might help to understand higher dimensional partitions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-05T23:14:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P81",
      "11P84",
      "28A25",
      "49J99",
      "49K99"
    ],
    "keywords": [
      "integer partitions",
      "understand higher dimensional partitions",
      "write partitions",
      "eulers identity",
      "optimal transportation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}