{
  "abstract": "Let $r$ and $n$ be two positive integers and $S=K[x_1,\\ldots,x_{n+r-1}]$, the ring of polynomials in $n+r-1$ variable, over a field $K$. We consider the squarefree monomial ideal $I_{n,r}:= x_1 \\cdots x_{r-1} (x_{r},\\ldots,x_{r+n-1}) \\subset S$ and we prove several results regarding the Hilbert depth of $S/I_{n,r}$. Also, we consider the special case $n=r$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.11691",
  "author_total": 2,
  "authors": [
    {
      "name": "Andreea I. Bordianu"
    },
    {
      "name": "Mircea Cimpoeas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4d9nsmxw2p5qd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.11691",
  "fulltext_url": null,
  "id": "4d9nsmxw2p5qd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.11691",
  "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": "W7168292845",
  "pdf_url": "https://arxiv.org/pdf/2607.11691",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4d9nsmxw2p5qd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2607.11691",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.11691"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Hilbert depth of a special class of squarefree monomial ideals",
  "title_text": "On the Hilbert depth of a special class of squarefree monomial ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/4d9nsmxw2p5qd",
  "venue": "arXiv",
  "versions": []
}