{
  "abstract": "We construct an explicit DG algebra structure on the minimal free resolution of the quotient of a polynomial ring by the edge ideal of any split graph (that is, a graph whose vertex set is a disjoint union of a clique and an independent set). The algebra structure is based on a simple combinatorial notion, which we call the fixing edge of a pair of edges, that directly captures the structure of the underlying graph. Our construction involves an explicit description of the minimal free resolution of the edge ideal of such a graph, including formulas for both the Betti numbers and the differentials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40540",
  "author_total": 4,
  "authors": [
    {
      "name": "David Bronshvayg"
    },
    {
      "name": "Rachel Diethorn"
    },
    {
      "name": "Mario Stinson-Maas"
    },
    {
      "name": "Reed Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5g6mhxa0sxfk4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40540",
  "fulltext_url": null,
  "id": "5g6mhxa0sxfk4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40540",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40540",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5g6mhxa0sxfk4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40540",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40540"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A DG algebra structure for the edge ideal of any split graph",
  "title_text": "A DG algebra structure for the edge ideal of any split graph",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/5g6mhxa0sxfk4",
  "venue": "arXiv",
  "versions": []
}