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PreprintCC BY 4.0arXiv

Premaniplexes of rank $3$ and $4$ as symmetry type graphs of maniplexes

  • Maruša Lekše
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Abstract

We show that every finite premaniplex of rank $3$ or $4$ is the symmetry type graph of a finite maniplex, settling the finite rank $3$ and $4$ case of the maniplex version of the symmetry type graph problem. The proof uses the fact that the universal string Coxeter groups of rank $3$ and $4$ are amalgams (of finite groups), hence they act on a tree, which allows us to use a lifting theorem of Potočnik and Spiga.

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Cite

BibTeXRIS
BibTeX
@misc{lekse2026premaniplexes,
  title = {{Premaniplexes of rank $3$ and $4$ as symmetry type graphs of maniplexes}},
  author = {Maruša Lekše},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13090},
  eprint = {2609.13090},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13090},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Premaniplexes of rank $3$ and $4$ as symmetry type graphs of maniplexes
AU  - Maruša Lekše
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.13090
UR  - https://arxiv.org/abs/2609.13090
AB  - We show that every finite premaniplex of rank $3$ or $4$ is the symmetry type graph of a finite maniplex, settling the finite rank $3$ and $4$ case of the maniplex version of the symmetry type graph problem. The proof uses the fact that the universal string Coxeter groups of rank $3$ and $4$ are amalgams (of finite groups), hence they act on a tree, which allows us to use a lifting theorem of Potočnik and Spiga.
ER  -