{
  "abstract": "We prove Bouvier's conjecture. More generally, an integer sequence $(a_n)_{n \\ge 0}$ with $a_0=d \\ge 0$ is realized by a unique factorization domain (UFD) $R$ with $\\dim R[X_1,\\ldots,X_n]=a_n$ for every $n \\ge 0$ if and only if $$ a_n+1\\le a_{n+1} \\le a_n+\\left\\lfloor\\frac{a_n+1}{n+1}\\right\\rfloor \\qquad(n\\ge0) $$ and $a_1 \\le 2d$ whenever $d \\ge 1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01887",
  "author_total": 3,
  "authors": [
    {
      "name": "Viet-Hoang Tran"
    },
    {
      "name": "Thieu N. Vo"
    },
    {
      "name": "Tan M. Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7yw28m9jm8tc8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01887",
  "fulltext_url": null,
  "id": "7yw28m9jm8tc8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01887",
  "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",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7207565289",
  "pdf_url": "https://arxiv.org/pdf/2609.01887",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7yw28m9jm8tc8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.01887",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01887"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Bouvier's Conjecture and Dimension Sequences of Unique Factorization Domains",
  "title_text": "Bouvier's Conjecture and Dimension Sequences of Unique Factorization Domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/7yw28m9jm8tc8",
  "venue": "arXiv",
  "versions": []
}