{
  "id": "2312.08114",
  "version": "v1",
  "published": "2023-12-13T13:01:34.000Z",
  "updated": "2023-12-13T13:01:34.000Z",
  "title": "A note on hook length equidistribution on arithmetic progressions",
  "authors": [
    "Joshua Males"
  ],
  "comment": "Short 8-page note",
  "categories": [
    "math.CO"
  ],
  "abstract": "In a recent paper, Bringmann, Craig, Ono, and the author showed that the number of $t$-hooks ($t\\geq2$) among all partitions of $n$ is not always asymptotically equidistributed on congruence classes $a \\pmod{b}$. In this short note, we clarify the situation of $t=1$, i.e. all hook lengths, and show that this case does give asymptotic equidistribution, closing the story of the distribution properties of $t$-hooks on congruence classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-13T13:01:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hook length equidistribution",
      "arithmetic progressions",
      "congruence classes",
      "short note",
      "asymptotic equidistribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}