{
  "abstract": "Building on the work of Pach, Rubin, and Tardos, we prove that every set of $n\\ge2$ points in the real plane with no three collinear contains at least $cn$ pairwise crossing segments with distinct endpoints, for an absolute constant $c>0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29449",
  "author_total": 1,
  "authors": [
    {
      "name": "Tim Gehrunger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6n6hea3k449z6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29449",
  "fulltext_url": null,
  "id": "6n6hea3k449z6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29449",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214284511",
  "pdf_url": "https://arxiv.org/pdf/2609.29449",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6n6hea3k449z6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29449",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29449"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Linear crossing families via dual levels",
  "title_text": "Linear crossing families via dual levels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/6n6hea3k449z6",
  "venue": "arXiv",
  "versions": []
}