{
  "abstract": "We show that the number of ways to tile a circular $n$-board (an annulus divided into $n$ curved unit square cells) with appropriately curved unit squares and curved (1,1)-fences is a Lucas number squared if $n$ is even and an odd-indexed Lucas number otherwise. A curved (1,1)-fence is composed of two curved unit squares separated by a gap in the shape of another curved unit square. This combinatorial interpretation of the Lucas numbers squared and the odd-indexed Lucas numbers allows us to obtain various identities concerning these sequences in a quick and lucid manner.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39599",
  "author_total": 2,
  "authors": [
    {
      "name": "Michael A. Allen"
    },
    {
      "name": "Kenneth Edwards"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cs0tywepb08xj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39599",
  "fulltext_url": null,
  "id": "cs0tywepb08xj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39599",
  "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.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39599",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cs0tywepb08xj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39599",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39599"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Tiling circular $n$-boards with squares and (1,1)-fences",
  "title_text": "Tiling circular n-boards with squares and (1,1)-fences",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/cs0tywepb08xj",
  "venue": "arXiv",
  "versions": []
}