{
  "abstract": "Let $G$ be a group of permutations of a set $Ω$. The relational complexity $\\mathrm{RC}(G)$ is the least integer $r\\geq 2$ such that the $G$-orbit of every finite tuple is determined by the $G$-orbits of its $r$-subtuples; there is currently only a small collection of groups $G$ for which $\\mathrm{RC}(G)$ is known precisely. In this paper we study the relational complexity of finite affine groups acting naturally on a $d$-dimensional vector space over $\\mathbb{F}_q$. We prove that every such group has relational complexity at most $d+2$ when $q>2$ and at most $d+1$ when $q=2$; we produce a complete classification of the primitive such groups for which these bounds are attained.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20077",
  "author_total": 3,
  "authors": [
    {
      "name": "Coen del Valle"
    },
    {
      "name": "Nick Gill"
    },
    {
      "name": "Pablo Spiga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/45asxznayynzt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20077",
  "fulltext_url": null,
  "id": "45asxznayynzt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20077",
  "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.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7222262067",
  "pdf_url": "https://arxiv.org/pdf/2610.20077",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/45asxznayynzt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20077",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20077"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the maximum relational complexity of affine groups",
  "title_text": "On the maximum relational complexity of affine groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/45asxznayynzt",
  "venue": "arXiv",
  "versions": []
}