{
  "abstract": "Suppose we have $r$ hypersurfaces in $\\mathbb{P}^m$ of degree $d$, whose defining polynomials are linearly independent and whose intersection is zero-dimensional. What is the maximum number of points in their intersection? This problem is motivated by computing the generalized Hamming weights of projective Reed-Muller codes, and a conjectured formula for this maximum was given in [21]. We prove the conjectured formula for arbitrary $m$ when $\\binom{m+d}{d}-\\binom{d+2}{2}<r\\leq\\binom{m+d}{d}$. We use the notion of Artinian reduction to reformulate the problem in terms of graded Artinian algebras and then apply combinatorial tools to bound their Hilbert functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01273",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuxin Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e1hbt0vaw8b8e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01273",
  "fulltext_url": null,
  "id": "e1hbt0vaw8b8e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01273",
  "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"
    ],
    [
      "arxiv",
      "math.AG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01273",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e1hbt0vaw8b8e.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01273",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01273"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Artinian reduction applied to the Largest Intersection Problem",
  "title_text": "Artinian reduction applied to the Largest Intersection Problem",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/e1hbt0vaw8b8e",
  "venue": "arXiv",
  "versions": []
}