A classification of rotary embeddings of multicycles
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910059906203648 |
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| author | Ding, Zhaochen Guo, Zheng Liu, Luyi |
| author_facet | Ding, Zhaochen Guo, Zheng Liu, Luyi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02808 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A classification of rotary embeddings of multicycles Ding, Zhaochen Guo, Zheng Liu, Luyi Combinatorics Group Theory 05C25 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. |
| title | A classification of rotary embeddings of multicycles |
| topic | Combinatorics Group Theory 05C25 |
| url | https://arxiv.org/abs/2603.02808 |