{
  "abstract": "Let $g(n)$ denote the largest number of facets of a full-dimensional $0/1$-polytope in $\\R^n$. We prove that there are absolute constants $c>0$ and $n_0$ such that $$ g(n)\\ge (cn)^{n/2}\\quad(n\\ge n_0). $$ This removes the logarithmic factor from the lower bound $\\bigl(cn/\\log n\\bigr)^{n/2}$ of Gatzouras, Giannopoulos, and Markoulakis. The proof compares a random sign polytope with two Rademacher rate bodies separated by a fixed level gap. Facets missing the inner body have uniformly small footprints on a flat patch of the outer body. A facet entering the inner body forces an empty buffered discrete cap. For shallow penetration, a likelihood-slab localization reduces the relevant range entropy and permits a conditional $\\varepsilon$-net argument; for deep penetration, a global discretization suffices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.17127",
  "author_total": 1,
  "authors": [
    {
      "name": "Omer Friedland"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1hq52bj1c91fk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.17127",
  "fulltext_url": null,
  "id": "1hq52bj1c91fk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.17127",
  "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",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7203751602",
  "pdf_url": "https://arxiv.org/pdf/2608.17127",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1hq52bj1c91fk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.17127",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.17127"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Log-Free Lower Bound for the Number of Facets of $0/1$-Polytopes",
  "title_text": "A Log-Free Lower Bound for the Number of Facets of 0/1-Polytopes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/1hq52bj1c91fk",
  "venue": "arXiv",
  "versions": []
}