{
  "id": "2303.13906",
  "version": "v1",
  "published": "2023-03-24T10:40:52.000Z",
  "updated": "2023-03-24T10:40:52.000Z",
  "title": "Some congruences for $(\\ell, k)$ and $(\\ell, k, r)$-regular partitions",
  "authors": [
    "T Kathiravan",
    "K Srinivas",
    "Usha K Sangale"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $b_{\\ell, k}(n), b_{\\ell, k, r}(n)$ count the number of $(\\ell, k)$, $(\\ell, k, r)$-regular partitions respectively. In this paper we shall derive infinite families of congruences for $b_{\\ell, k}(n)$ modulo $2$ when $ (\\ell, k) = (3,8), (4, 7)$, for $b_{\\ell, k}(n)$ modulo $8$, modulo $9$ and modulo $12$ when $(\\ell, k) = (4, 9)$ and $b_{\\ell, k, r}(n)$ modulo $2$ when $(\\ell, k, r) = (3, 5, 8)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-24T10:40:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P83",
      "05A17"
    ],
    "keywords": [
      "regular partitions",
      "congruences",
      "derive infinite families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}