{
  "abstract": "Let $S$ be a minimally four-generated numerical semigroup that is nearly Gorenstein but not almost symmetric, and let $R=k[S]$ over an arbitrary field $k$. We prove that the defining ideal of $R$ has four or five minimal generators when $R$ has Cohen--Macaulay type two, and exactly six when it has type three. Thus the total Betti sequence over the four-variable polynomial presentation ring is one of $$(1,4,5,2),\\quad (1,5,6,2),\\quad (1,6,8,3),$$ and all three possibilities occur. The type-three argument uses a canonical-ideal exact sequence, a chain-level comparison on $\\operatorname{Tor}$, and a codimension-three Gorenstein reduction. The resulting classification gives an affirmative answer, over every field, to Moscariello and Strazzanti's Question 4.3 on four-generated nearly Gorenstein numerical semigroups that are not almost symmetric.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05788",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhi-Lin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1epdqddqsvr3p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05788",
  "fulltext_url": null,
  "id": "1epdqddqsvr3p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05788",
  "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/2611.05788",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1epdqddqsvr3p.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05788",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05788"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Betti Sequences of Four-Generated Non-Almost-Symmetric Nearly Gorenstein Numerical Semigroup Rings",
  "title_text": "Betti Sequences of Four-Generated Non-Almost-Symmetric Nearly Gorenstein Numerical Semigroup Rings",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:29Z",
  "url": "https://research.draconitic.com/paper/1epdqddqsvr3p",
  "venue": "arXiv",
  "versions": []
}