{
  "abstract": "A pentagonal geometry PENT(k,r) is a k-uniform, r-regular partial linear space with the property that the set of points not collinear with a given point x is itself a line in the geometry. The existence spectrum of these geometries is known; we begin the study of automorphisms of these structures in the case k=3. We determine the spectrum of pentagonal geometries PENT(3,r) with either a cyclic or reverse automorphism to be r = 1 or 10 (mod 12). In addition, we show that there are 584 pairwise non-isomorphic PENT(3,7)s and classify them by the orders of their automorphism groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01390",
  "author_total": 2,
  "authors": [
    {
      "name": "Grahame Erskine"
    },
    {
      "name": "Terry S. Griggs"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7retgj6njmcsx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01390",
  "fulltext_url": null,
  "id": "7retgj6njmcsx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01390",
  "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",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7216302362",
  "pdf_url": "https://arxiv.org/pdf/2610.01390",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7retgj6njmcsx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01390",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01390"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Automorphisms of pentagonal geometries with block size 3",
  "title_text": "Automorphisms of pentagonal geometries with block size 3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/7retgj6njmcsx",
  "venue": "arXiv",
  "versions": []
}