{
  "abstract": "Recently, Andrews and El Bachraoui introduced partition-counting functions $a_2(n)$ and $b_2(n)$, together with their signed analogues $a'_2(n)$ and $b'_2(n)$, and proved that $a'_2(n), b'_2(n)>0$ for all $n\\geq 3$. For $m\\geq 2$, the latter functions extend naturally to $a'_m(n)$ and $b'_m(n)$, defined by \\begin{align*} \\sum_{n\\geq 0} a'_m(n)q^n &= -\\frac{q}{1-q} \\frac{(q^m;q^m)_\\infty}{(q;q^m)_\\infty} +\\frac{q}{(1-q)^2},\\\\ \\sum_{n\\geq 0} b'_m(n)q^n &= -\\frac{q(1-q^{m-1})}{1-q} \\frac{(q^{2m};q^m)_\\infty}{(q;q^m)_\\infty} +\\frac{q}{1-q} \\left( \\frac{1}{1-q} -\\frac{q^{m-1}}{1-q^{m+1}} \\right). \\end{align*} They asked whether there exists an integer $m>2$ for which $a'_m(n)$ is eventually positive, and posed the same question for $b'_m(n)$. In this paper, we resolve these two questions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02389",
  "author_total": 2,
  "authors": [
    {
      "name": "Meng-Yao Li"
    },
    {
      "name": "Su-Ping Cui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77cwer66yhhx7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02389",
  "fulltext_url": null,
  "id": "77cwer66yhhx7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02389",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02389",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77cwer66yhhx7.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02389",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02389"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Infinitely many negative terms in two weighted partition sequences",
  "title_text": "Infinitely many negative terms in two weighted partition sequences",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/77cwer66yhhx7",
  "venue": "arXiv",
  "versions": []
}