{
  "id": "2109.10344",
  "version": "v1",
  "published": "2021-09-21T17:56:43.000Z",
  "updated": "2021-09-21T17:56:43.000Z",
  "title": "Distribution of certain $\\ell$-regular partitions and triangular numbers",
  "authors": [
    "Chiranjit Ray"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $pod_{\\ell}(n)$ be the number of $\\ell$-regular partitions of $n$ with distinct odd parts. In this article, prove that for any positive integer $k$, the set of non-negative integers $n$ for which $pod_{\\ell}(n)\\equiv 0 \\pmod{p^{k}}$ has density one under certain conditions on $\\ell$ and $p$. For $p \\in \\{3,5,7\\}$, we also exhibit multiplicative identities for $pod_{p}(n)$ modulo $p.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-21T17:56:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P83",
      "11F11",
      "11F20"
    ],
    "keywords": [
      "regular partitions",
      "triangular numbers",
      "distribution",
      "distinct odd parts",
      "non-negative integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}