{
  "abstract": "We study numerical semigroups whose defining ideals admit determinantal presentations by the $2\\times2$ minors of a $2\\times n$ matrix. A conjecture of Cuong, Kien, Matsuoka, and Truong relates such presentations to arithmetic progressions of pseudo-Frobenius numbers. We prove a numerical criterion for this determinantal presentation, reducing the conjecture to a problem on factorizations of maximal elements of an Apéry set in the numerical semigroup. As an application, we verify the conjecture in embedding dimension four under a unique factorization assumption on an Apéry set.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18136",
  "author_total": 2,
  "authors": [
    {
      "name": "Satoshi Murai"
    },
    {
      "name": "Kou Takahashi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f216k76wx3ewt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18136",
  "fulltext_url": null,
  "id": "f216k76wx3ewt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18136",
  "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.AC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.18136",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f216k76wx3ewt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18136",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18136"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A criterion for determinantal presentations of numerical semigroup rings",
  "title_text": "A criterion for determinantal presentations of numerical semigroup rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/f216k76wx3ewt",
  "venue": "arXiv",
  "versions": []
}