{
  "abstract": "Let $R_{n,p}$ be the determinantal hypersurface ring defined by the determinant of a generic $n \\times n$ matrix in characteristic $p$ where $n \\geq 2$. In this paper, we obtain explicit bounds for the $F$-signature of $R_{n,p}$. For the upper bound, we prove that this $F$-signature is decreasing in $n$, so the $F$-signature of $R_{2,p}$ serves as an upper bound, which is $2/3$. For the lower bound, we find a toric degeneration $B_n$ of $R_{n,p}$, so the $F$-signature of $B_n$ serves as a lower bound. This $F$-signature can be computed using either Gröbner basis or Han-Monsky machinery, and its value is $\\frac{(n!)^2}{(2n-1)!}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32955",
  "author_total": 4,
  "authors": [
    {
      "name": "Hang Huang"
    },
    {
      "name": "Cheng Meng"
    },
    {
      "name": "Suchitra Pande"
    },
    {
      "name": "Yevgeniya Tarasova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9tdhwjq5gzgwv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32955",
  "fulltext_url": null,
  "id": "9tdhwjq5gzgwv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32955",
  "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",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7214734251",
  "pdf_url": "https://arxiv.org/pdf/2609.32955",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9tdhwjq5gzgwv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:20Z",
      "native_id": "2609.32955",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32955"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The F-signature of Determinantal Rings",
  "title_text": "The F-signature of Determinantal Rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:20Z",
  "url": "https://research.draconitic.com/paper/9tdhwjq5gzgwv",
  "venue": "arXiv",
  "versions": []
}