The Hurwitz existence problem and the prime-degree conjecture: A computational perspective
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917133401718784 |
|---|---|
| author | Wang, Yiru Li, Bingqian Zhou, Yi Wei, Zhiqiang Ye, Yu Shi, Yiqian Xu, Bin |
| author_facet | Wang, Yiru Li, Bingqian Zhou, Yi Wei, Zhiqiang Ye, Yu Shi, Yiqian Xu, Bin |
| contents | We investigate the Hurwitz existence problem from a computational viewpoint. Leveraging the symmetric-group algorithm by Zheng and building upon implementations originally developed by Baroni, we achieve a complete and non-redundant enumeration of all non-realizable partition triples for positive integers up to $31$. These results are further categorized into four types according to their underlying mathematical structure; it is observed that nearly nine-tenths of them can be explained by known theoretical results. As an application, we verify the prime-degree conjecture for all primes less than $32$. In light of the exponential memory growth inherent in existing computational approaches -- which limits their feasibility at higher degrees -- we propose a novel software architecture designed to stabilize memory usage, thereby facilitating further detection of exceptional cases in the Hurwitz existence problem. The complete dataset of non-realizable partition triples, along with our implementation, will been made public on GitHub. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Hurwitz existence problem and the prime-degree conjecture: A computational perspective Wang, Yiru Li, Bingqian Zhou, Yi Wei, Zhiqiang Ye, Yu Shi, Yiqian Xu, Bin Group Theory 05A17, 20B35, 57M12 We investigate the Hurwitz existence problem from a computational viewpoint. Leveraging the symmetric-group algorithm by Zheng and building upon implementations originally developed by Baroni, we achieve a complete and non-redundant enumeration of all non-realizable partition triples for positive integers up to $31$. These results are further categorized into four types according to their underlying mathematical structure; it is observed that nearly nine-tenths of them can be explained by known theoretical results. As an application, we verify the prime-degree conjecture for all primes less than $32$. In light of the exponential memory growth inherent in existing computational approaches -- which limits their feasibility at higher degrees -- we propose a novel software architecture designed to stabilize memory usage, thereby facilitating further detection of exceptional cases in the Hurwitz existence problem. The complete dataset of non-realizable partition triples, along with our implementation, will been made public on GitHub. |
| title | The Hurwitz existence problem and the prime-degree conjecture: A computational perspective |
| topic | Group Theory 05A17, 20B35, 57M12 |
| url | https://arxiv.org/abs/2512.06545 |