{
  "abstract": "A symmetric $(v,k,λ)$-design is said to be $f$-pyramidal, with $f<v-1$, under the action of a group $G$ if $G$ acts as an automorphism group fixing $f$ points and acting sharply transitively on the remaining ones. We show that, necessarily, $f\\leq v -2(k-λ)$. In particular, for a Hadamard design with parameters $(v,k,λ)=(4m-1, 2m-1, m-1)$, for some $m\\in\\mathbb{N}$, it follows that $f\\leq 2m-1$. Recently, working on the complement design, the family $P$ of Hadamard $(4m-1,2m-1,m-1)$-designs admitting an abelian $(2m-1)$-pyramidal automorphism group $G$ has been completely determined in the case $m=2^{k}>1$. In this paper, we generalize that result by showing that $P$ coincides with the family of Hadamard $(4m-1,2m-1,m-1)$-designs admitting a $(2m-1)$-pyramidal automorphism group, without assuming either that the group is abelian or that $m$ is a power of $2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04858",
  "author_total": 1,
  "authors": [
    {
      "name": "Tommaso Traetta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1bmgxang5tatn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04858",
  "fulltext_url": null,
  "id": "1bmgxang5tatn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04858",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.04858",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1bmgxang5tatn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04858",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04858"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Characterizing pyramidal Hadamard designs with the largest number of fixed points",
  "title_text": "Characterizing pyramidal Hadamard designs with the largest number of fixed points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/1bmgxang5tatn",
  "venue": "arXiv",
  "versions": []
}