{
  "abstract": "If $S$ is a numerical semigroup, then we denote by $m(S)$, $F(S)$ and $\\mathrm{PF}(S)$ its multiplicity, its Frobenius number and its set of pseudo-Frobenius numbers, respectively. Let $\\mathcal P$ be a finite nonempty set of positive integers. In this paper, we prove that $\\mathcal C(\\mathcal P)=\\{S\\mid F(S)=\\max(\\mathcal P),\\ \\mathcal P\\subseteq\\mathrm{PF}(S)\\}$ is a covariety. The associated tree provides algorithms to compute $\\mathcal C(\\mathcal P)$, its elements with a prescribed type or genus, and the set of numerical semigroups $S$ satisfying $\\mathrm{PF}(S)=\\mathcal P$. We show that every element of $\\mathcal C(\\mathcal P)$ has a unique minimal system of generators relative to $\\mathcal C(\\mathcal P)$, and we call its cardinality the $\\mathcal C(\\mathcal P)$-rank. Finally, we characterize the elements of $\\mathcal C(\\mathcal P)$ with $\\mathcal C(\\mathcal P)$-rank one.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.09425",
  "author_total": 2,
  "authors": [
    {
      "name": "William Giovanni Hernández-Yanes"
    },
    {
      "name": "José Carlos Rosales"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0dp7rrz6jwnhw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.09425",
  "fulltext_url": null,
  "id": "0dp7rrz6jwnhw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.09425",
  "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.AC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.09425",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0dp7rrz6jwnhw.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.09425",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.09425"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The covariety of numerical semigroups with some prescribed pseudo-Frobenius numbers",
  "title_text": "The covariety of numerical semigroups with some prescribed pseudo-Frobenius numbers",
  "type": "preprint",
  "updated_at": "2026-11-11T06:20:56Z",
  "url": "https://research.draconitic.com/paper/0dp7rrz6jwnhw",
  "venue": "arXiv",
  "versions": []
}