{
  "id": "1306.0136",
  "version": "v2",
  "published": "2013-06-01T18:36:33.000Z",
  "updated": "2013-06-06T01:05:21.000Z",
  "title": "Congruences for 9-regular partitions modulo 3",
  "authors": [
    "William J. Keith"
  ],
  "comment": "7 pages. v2: added citations and proof of one conjecture from a reader. Submitted version",
  "categories": [
    "math.CO"
  ],
  "abstract": "It is proved that the number of 9-regular partitions of n is divisible by 3 when n is congruent to 3 mod 4, and by 6 when n is congruent to 13 mod 16. An infinite family of congruences mod 3 holds in other progressions modulo powers of 4 and 5. A collection of conjectures includes two congruences modulo higher powers of 2 and a large family of \"congruences with exceptions\" for these and other regular partitions mod 3.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-06T01:05:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P83"
    ],
    "keywords": [
      "partitions modulo",
      "congruences modulo higher powers",
      "regular partitions mod",
      "progressions modulo powers",
      "conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.0136K"
    }
  }
}