{
  "id": "2404.02367",
  "version": "v1",
  "published": "2024-04-02T23:54:55.000Z",
  "updated": "2024-04-02T23:54:55.000Z",
  "title": "A note on the exact formulas for certain $2$-color partitions",
  "authors": [
    "Russelle Guadalupe"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Let $p\\leq 23$ be a prime and $a_p(n)$ count the number of partitions of $n$ using two colors where one of the colors only has parts divisible by $p$. Using a result of Sussman, we derive the exact formula for $a_p(n)$ and obtain an asymptotic formula for $\\log a_p(n)$. Our results partially extend the work of Mauth, who proved the asymptotic formula for $\\log a_2(n)$ conjectured by Banerjee et al.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-02T23:54:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P55",
      "11P82",
      "05A16"
    ],
    "keywords": [
      "exact formula",
      "color partitions",
      "asymptotic formula",
      "results partially extend"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}