{
  "abstract": "An arrangement of $n$ lines in the plane defines cells, i.e., connected components of the complement of the arrangement. Answering a question of Volkmar Welker we show that, apart from two special cases, there is always a line $L$ in the arrangement such that one of the open halfplanes whose boundary is $L$ contains more than half of the bounded cells of the arrangement. We also consider some unusual discrepancy problems that are related to this question.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23203",
  "author_total": 1,
  "authors": [
    {
      "name": "Imre Bárány"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2d4az1my0da9d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23203",
  "fulltext_url": null,
  "id": "2d4az1my0da9d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23203",
  "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.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214055472",
  "pdf_url": "https://arxiv.org/pdf/2609.23203",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2d4az1my0da9d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23203",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23203"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Line arrangements, bounded cells, and discrepancy",
  "title_text": "Line arrangements, bounded cells, and discrepancy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/2d4az1my0da9d",
  "venue": "arXiv",
  "versions": []
}