{
  "abstract": "In 2018, Andrews defined and studied the partition function $\\mathcal{EO}(n)$, which counts the number of partitions of $n$ where each even part is less than each odd part. Thereafter, Uncu considered a different subset of such partitions, namely those partitions counted by $\\mathcal{EO}(n)$ where there are no repeated even parts (we denote the number of such partitions by $\\mathcal{EO}_u(n)$). In this paper, we prove several congruences modulo powers of $2$ for $\\mathcal{EO}_u(n)$. We also prove some infinite families of congruences as well as a recurrence for the number of this class of partitions. Our methods involve elementary, algorithmic, and modular form techniques.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37920",
  "author_total": 4,
  "authors": [
    {
      "name": "Nayandeep Deka Baruah"
    },
    {
      "name": "Hirakjyoti Das"
    },
    {
      "name": "Manjil P. Saikia"
    },
    {
      "name": "Abhishek Sarma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7qvxfdhf2zev0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37920",
  "fulltext_url": null,
  "id": "7qvxfdhf2zev0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37920",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7214943976",
  "pdf_url": "https://arxiv.org/pdf/2609.37920",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7qvxfdhf2zev0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37920",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37920"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Congruences for the Andrews--Uncu partition function $\\mathcal{EO}_u(n)$",
  "title_text": "Congruences for the Andrews--Uncu partition function ℰ𝒪_u(n)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/7qvxfdhf2zev0",
  "venue": "arXiv",
  "versions": []
}