{
  "abstract": "We present a method for partitioning the solution space of statements in extremal set theory. Compared with domain-agnostic partitioning methods like look-ahead, we perform case analysis on the strategies by which a candidate solution can be constructed. We demonstrate that our approach can decompose problems in extremal set theory more effectively than look-ahead. Combining this new partitioning strategy with an exact proof-producing MILP solver, we are able to verify larger finite cases of Chvátal's Conjecture---a long-standing open question in extremal combinatorics---compared to previous work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.06432",
  "author_total": 6,
  "authors": [
    {
      "name": "Jesse Looney"
    },
    {
      "name": "Jonah McDonald"
    },
    {
      "name": "Allison Klingler"
    },
    {
      "name": "Gloria Wu"
    },
    {
      "name": "Jonad Pulaj"
    },
    {
      "name": "Haoze Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5g50rtk43jpt1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.06432",
  "fulltext_url": null,
  "id": "5g50rtk43jpt1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.06432",
  "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",
      "cs.DM"
    ],
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      "arxiv",
      "cs.LO"
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      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.06432",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5g50rtk43jpt1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2608.06432",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.06432"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Solution Space Partitioning for Extremal Set Theory",
  "title_text": "Solution Space Partitioning for Extremal Set Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/5g50rtk43jpt1",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.34727/2026/isbn.978-3-85448-093-8_75",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}