{
  "id": "1406.2583",
  "version": "v2",
  "published": "2014-06-10T15:14:28.000Z",
  "updated": "2014-07-09T04:09:09.000Z",
  "title": "On the Enumeration of $(s,s+1,s+2)$-Core Partitions",
  "authors": [
    "Jane Y. X. Yang",
    "Michael X. X. Zhong",
    "Robin D. P. Zhou"
  ],
  "comment": "20 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Anderson established a connection between core partitions and order ideals of certain posets by mapping a partition to its $\\beta$-set. In this paper, we give a characterization of the poset $P_{(s,s+1,s+2)}$ whose order ideals correspond to $(s,s+1,s+2)$-core partitions. Using this characterization, we obtain the number of $(s,s+1,s+2)$-core partitions, the maximum size and the average size of an $(s,s+1,s+2)$-core partition, confirming three conjectures posed by Amdeberhan.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-09T04:09:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A17",
      "06A07"
    ],
    "keywords": [
      "core partition",
      "enumeration",
      "order ideals correspond",
      "characterization",
      "connection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.2583Y"
    }
  }
}