{
  "id": "2204.05592",
  "version": "v1",
  "published": "2022-04-12T07:48:46.000Z",
  "updated": "2022-04-12T07:48:46.000Z",
  "title": "A Central Limit Theorem for Integer Partitions into Small Powers",
  "authors": [
    "Gabriel F. Lipnik",
    "Manfred G. Madritsch",
    "Robert F. Tichy"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "The study of the well-known partition function $p(n)$ counting the number of solutions to $n = a_{1} + \\dots + a_{\\ell}$ with integers $1 \\leq a_{1} \\leq \\dots \\leq a_{\\ell}$ has a long history in combinatorics. In this paper, we study a variant, namely partitions of integers into \\begin{equation*} n=\\lfloor a_1^\\alpha\\rfloor + \\cdots + \\lfloor a_\\ell^\\alpha\\rfloor \\end{equation*} with $1\\leq a_1 < \\cdots < a_\\ell$ and some fixed $0 < \\alpha < 1$. In particular, we prove a central limit theorem for the number of summands in such partitions, using the saddle point method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-12T07:48:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P82",
      "05A17",
      "60F05"
    ],
    "keywords": [
      "central limit theorem",
      "integer partitions",
      "small powers",
      "well-known partition function",
      "saddle point method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}