{
  "abstract": "We investigate arithmetic and combinatorial properties of the function $a(n)$, which is the signed number of partitions of $n$ into exactly two distinct part sizes, each occurring an odd number of times. We prove that $a(n)\\ge 0$ for all $n$, establishing a positivity phenomenon for a signed partition function arising from a double Lambert series. Furthermore, we show that $a(n)$ satisfies nontrivial divisibility properties modulo $3$. The results reveal unexpected arithmetic regularity in a family of partition functions defined by odd multiplicity constraints and restricted support.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Ramanujan Journal, 71: 23 (2026)",
  "arxiv": "2609.33770",
  "author_total": 1,
  "authors": [
    {
      "name": "Mircea Merca"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ekahwvxk664bd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33770",
  "fulltext_url": null,
  "id": "ekahwvxk664bd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33770",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.33770",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ekahwvxk664bd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.33770",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33770"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The two-block odd partition function",
  "title_text": "The two-block odd partition function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/ekahwvxk664bd",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s11139-026-01426-1",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}