{
  "abstract": "We prove a conjecture of András Bezdek on plank coverings of square annuli. A plank in a Euclidean space is the closed region between two distinct parallel hyperplanes, and its width is the distance between them. Let $Q$ be a unit square and let $H$ be a square of side length $1/2$ whose sides are parallel to those of $Q$. Then every finite family of planks covering $Q\\setminus H$ has total width at least $1$. More generally, if an axis-parallel box with side lengths $h_1,\\ldots,h_d$ is removed from the unit cube in $\\mathbb{R}^d$ and $\\sum_jh_j = d-1$, then every finite plank covering of the remaining set has total width at least one. The bounds are sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00379",
  "author_total": 2,
  "authors": [
    {
      "name": "Egor Bakaev"
    },
    {
      "name": "Alexander Polyanskii"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/73pejehtgn2k5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00379",
  "fulltext_url": null,
  "id": "73pejehtgn2k5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00379",
  "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"
    ],
    [
      "arxiv",
      "math.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00379",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/73pejehtgn2k5.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00379",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00379"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A sharp plank theorem for cube annuli",
  "title_text": "A sharp plank theorem for cube annuli",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/73pejehtgn2k5",
  "venue": "arXiv",
  "versions": []
}