{
  "id": "2207.07513",
  "version": "v1",
  "published": "2022-07-15T14:57:38.000Z",
  "updated": "2022-07-15T14:57:38.000Z",
  "title": "Enumeration of Partitions modulo 4",
  "authors": [
    "Aditya Khanna"
  ],
  "comment": "36 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The number of standard Young tableaux possible of shape corresponding to a partition $\\lambda$ is called the dimension of the partition and is denoted by $f^{\\lambda}$. Partitions with odd dimensions were enumerated by McKay and were further classified by Macdonald. Let $a_i(n)$ be the number of partitions of $n$ with dimension congruent to $i$ modulo 4. In this paper, we refine Macdonald's and McKay's results by calculating $a_1(n)$ and $a_3(n)$ when $n$ has no consecutive 1s in its binary expansion or when the sum of binary digits of $n$ is 2 and providing values for $a_2(n)$ for all $n$. We also present similar results for irreducible representations of alternating groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-15T14:57:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "20C30"
    ],
    "keywords": [
      "partitions modulo",
      "enumeration",
      "standard young tableaux",
      "odd dimensions",
      "similar results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}