{
  "abstract": "The balance constant is a poset parameter measuring how well random linear extensions can be split according to their relative order on two elements. We give an $\\varepsilon$-improvement for the balance constant over the bound by Brightwell, Felsner and Trotter (1995), for some small $\\varepsilon>0$. This is the first general result towards the $\\frac{1}{3}$--$\\frac{2}{3}$ conjecture in over 30 years.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30888",
  "author_total": 4,
  "authors": [
    {
      "name": "Max Aires"
    },
    {
      "name": "Swee Hong Chan"
    },
    {
      "name": "Igor Pak"
    },
    {
      "name": "Greta Panova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0fn6b4q4kc06a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30888",
  "fulltext_url": null,
  "id": "0fn6b4q4kc06a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30888",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214603325",
  "pdf_url": "https://arxiv.org/pdf/2609.30888",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0fn6b4q4kc06a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2609.30888",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30888"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Breaking the Infinite Barrier in the $\\frac{1}{3}$--$\\frac{2}{3}$ Conjecture",
  "title_text": "Breaking the Infinite Barrier in the 1/3--2/3 Conjecture",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/0fn6b4q4kc06a",
  "venue": "arXiv",
  "versions": []
}