{
  "abstract": "Fix a square-free monomial $m = x_{i_1} \\cdots x_{i_s}$ in $S = \\K[x_1, \\dots, x_n]$, where $\\K$ is a field. The ideal generated by all square-free monomials that are Borel moves of $m$ is referred to as the \\emph{square-free principal Borel ideal}, denoted by $\\mathrm{sfBorel}(m)$. While the Waldschmidt constant of $\\mathrm{sfBorel}(m)$ has been partially studied in the literature, we consider the remaining cases and provide bounds for the Waldschmidt constant of $\\mathrm{sfBorel}(m)$. In some cases, we explicitly compute its exact value. Furthermore, we study this invariant for square-free Borel and square-free lex-segment ideals, establishing both bounds and exact values for special cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32524",
  "author_total": 3,
  "authors": [
    {
      "name": "Ajay Kumar"
    },
    {
      "name": "Rajiv Kumar"
    },
    {
      "name": "Paramhans Kushwaha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5vgc9pk3883f8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32524",
  "fulltext_url": null,
  "id": "5vgc9pk3883f8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32524",
  "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": "W7214742070",
  "pdf_url": "https://arxiv.org/pdf/2609.32524",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5vgc9pk3883f8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32524",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32524"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Waldschmidt constant of square-free principal Borel ideals",
  "title_text": "The Waldschmidt constant of square-free principal Borel ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/5vgc9pk3883f8",
  "venue": "arXiv",
  "versions": []
}