{
  "id": "1407.5134",
  "version": "v2",
  "published": "2014-07-18T23:35:40.000Z",
  "updated": "2015-02-06T14:23:20.000Z",
  "title": "Armstrong's Conjecture for $(k, mk + 1)$-Core Partitions",
  "authors": [
    "Amol Aggarwal"
  ],
  "comment": "17 pages, 3 figures",
  "journal": "European Journal of Combinatorics 47, 54-67 (2015)",
  "doi": "10.1016/j.ejc.2015.01.008",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "A conjecture of Armstrong states that if $\\gcd (a, b) = 1$, then the average size of an $(a, b)$-core partition is $(a - 1)(b - 1)(a + b + 1) / 24$. Recently, Stanley and Zanello used a recursive argument to verify this conjecture when $a = b - 1$. In this paper we use a variant of their method to establish Armstrong's conjecture in the more general setting where $a$ divides $b - 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-18T23:35:40.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-06T14:23:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "core partition",
      "armstrong states",
      "establish armstrongs conjecture",
      "recursive argument"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.5134A"
    }
  }
}