A classification of rotary embeddings of multicycles
Abstract
We classify rotary (orientably-regular) maps whose underlying graphs are multicycles. For the multicycle $\mathrm{C}_n^{(λ)}$ of length $n$ and edge-multiplicity $λ$, we determine all rotary embeddings for $n\geqslant 3$ and $λ\geqslant 2$. When $n$ is odd, there is a unique isomorphism class; when $n$ is even, the embeddings form a family $\mathcal{M}_n^{(λ)}(i,j)$ parameterized by integer pairs $(i,j)$ satisfying explicit congruence conditions.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Graph Theory Research
Mathematics and Applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 3 March 2026
- Language
- EN
- Document type
- Preprint