{
  "abstract": "Andrews and Dastidar introduced the statistic $\\SOME(n)$, defined as the difference between the sum of all odd parts and the sum of all even parts occurring in the partitions of $n$, and investigated its arithmetic properties. Motivated by their work, Baruah and Gogoi defined two analogous statistics for overpartitions, namely $\\OSOMEo(n)$ and $\\OSOMEe(n)$, which record the sums of all odd and all even overlined parts, respectively. They established several congruences for these statistics and their difference, and proposed a conjecture on congruences modulo $7$. In this paper, we prove their conjecture by elementary $q$-series methods. Our proof combines two specializations of Watson's quintuple product identity, a $(p,k)$-parameterization of divisor-sum series, and termwise logarithmic differentiation",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27350",
  "author_total": 3,
  "authors": [
    {
      "name": "Eric H. Liu"
    },
    {
      "name": "X. L. Liu"
    },
    {
      "name": "Olivia X. M. Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3165xpxtpnhy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27350",
  "fulltext_url": null,
  "id": "e3165xpxtpnhy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27350",
  "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",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7214201946",
  "pdf_url": "https://arxiv.org/pdf/2609.27350",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3165xpxtpnhy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27350",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27350"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A proof of the Baruah--Gogoi conjecture on sums of odd and even overlined parts",
  "title_text": "A proof of the Baruah--Gogoi conjecture on sums of odd and even overlined parts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/e3165xpxtpnhy",
  "venue": "arXiv",
  "versions": []
}