{
  "id": "2404.04588",
  "version": "v1",
  "published": "2024-04-06T10:56:23.000Z",
  "updated": "2024-04-06T10:56:23.000Z",
  "title": "On the biases and asymptotics of partitions with finite choices of parts",
  "authors": [
    "Jiyou Li",
    "Sicheng Zhao"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Biases in integer partitions have been studied recently. For three disjoint subsets $R,S,I$ of positive integers, let $p_{RSI}(n)$ be the number of partitions of $n$ with parts from $R\\cup S\\cup I$ and $p_{R>S,I}(n)$ be the number of such partitions with more parts from $R$ than that from $S$. In this paper, in the case that $R,S,I$ are finite we obtain a concrete formula of the asymptotic ratio of $p_{R>S,I}(n)$ to $p_{RSI}(n)$. We also propose a conjecture in the case that $R,S$ are certain infinite arithmetic progressions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-06T10:56:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P81"
    ],
    "keywords": [
      "finite choices",
      "infinite arithmetic progressions",
      "disjoint subsets",
      "asymptotic ratio",
      "integer partitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}