{
  "abstract": "We study weak tiling by finite unions of pairwise non-overlapping unit cubes in $\\mathbb R^d$ that are not necessarily axis-parallel. We obtain a weak-tiling analogue of Keller's classical theorem, which gives a structural restriction on the support of any weak tiling measure associated with the unit cube. This allows us to derive geometric restrictions on configurations of cubes whose union admits a weak tiling. As an application, we prove Fuglede's conjecture for unions of three non-overlapping unit squares in $\\mathbb R^2$ as well as unions of two non-overlapping axis-parallel unit cubes in any dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34852",
  "author_total": 4,
  "authors": [
    {
      "name": "Tianyu Chen"
    },
    {
      "name": "Shilei Fan"
    },
    {
      "name": "Mihail N. Kolountzakis"
    },
    {
      "name": "Chun-Kit Lai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdm6e62rfdkhs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34852",
  "fulltext_url": null,
  "id": "cdm6e62rfdkhs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34852",
  "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.CA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7214781802",
  "pdf_url": "https://arxiv.org/pdf/2609.34852",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdm6e62rfdkhs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34852",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34852"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weak Tiling by Unions of Non-overlapping Unit Cubes",
  "title_text": "Weak Tiling by Unions of Non-overlapping Unit Cubes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/cdm6e62rfdkhs",
  "venue": "arXiv",
  "versions": []
}