Hypertopes with prescribed diagram symmetries

Abstract

Let 𝒢 be a finite connected simple graph with at least two vertices. We construct a finite regular hypertope Γ whose diagram is the graph 𝒢 with every edge labelled by $4$, and for which Cor(Γ)/Aut(Γ) ≅ Aut(𝒢). This shows that any possible group of diagram symmetries can be realized by the correlations of a hypertope. The construction uses a group generated by involutions, with nilpotency class two, exponent four and commutator relations dictated by the defining graph.

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BibTeX RIS

BibTeX

@misc{leemans2026hypertopes,
  title = {{Hypertopes with prescribed diagram symmetries}},
  author = {Dimitri Leemans and Pablo Spiga and Philippe Tranchida},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09711},
  eprint = {2610.09711},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09711},
}

RIS

TY  - UNPB
TI  - Hypertopes with prescribed diagram symmetries
AU  - Dimitri Leemans
AU  - Pablo Spiga
AU  - Philippe Tranchida
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09711
UR  - https://arxiv.org/abs/2610.09711
AB  - Let 𝒢 be a finite connected simple graph with at least two vertices. We construct a finite regular hypertope Γ whose diagram is the graph 𝒢 with every edge labelled by $4$, and for which Cor(Γ)/Aut(Γ) ≅ Aut(𝒢). This shows that any possible group of diagram symmetries can be realized by the correlations of a hypertope. The construction uses a group generated by involutions, with nilpotency class two, exponent four and commutator relations dictated by the defining graph.
ER  -

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