{
  "abstract": "A resolving set in a graph is a set of landmarks whose distance vectors distinguish all vertices. We use information theory to prove lower bounds for metric dimension and class dimension in distance-regular graphs and association schemes arising from finite geometry. The core idea is that, for a fixed landmark, a random object usually lies in one overwhelmingly likely distance or relation class. For classical dual polar graphs, with rank and type fixed and $q\\to\\infty$ through the admissible field orders, we prove $μ(Γ(q,d,e))=Θ_{d,e}(q^e)$ for $d\\geq 2$ and $e>0$. The lower bound uses opposition as the typical distance. For the upper bound, we take, for each of a constant number of $(d-1)$-dimensional singular subspaces, all generators containing it. For Grassmann graphs, bilinear forms graphs, and attenuated-space schemes, we obtain lower bounds of the same exponential order as the known incidence constructions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27788",
  "author_total": 1,
  "authors": [
    {
      "name": "Maximiliano Vazquez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56n0wz6c0whem.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27788",
  "fulltext_url": null,
  "id": "56n0wz6c0whem",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27788",
  "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": "W7204851193",
  "pdf_url": "https://arxiv.org/pdf/2608.27788",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56n0wz6c0whem.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27788",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27788"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Default-Distance Entropy and Metric Dimension in Finite Geometries",
  "title_text": "Default-Distance Entropy and Metric Dimension in Finite Geometries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/56n0wz6c0whem",
  "venue": "arXiv",
  "versions": []
}