Nullhomotopic and Generating Knight's Tours on Non-Orientable Surfaces
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911910557908992 |
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| author | Forrest, Bradley Lague, Zachary |
| author_facet | Forrest, Bradley Lague, Zachary |
| contents | We investigate closed knight's tours on Möbius strip and Klein bottle chess boards. In particular, we characterize the board dimensions that admit tours that are nullhomotopic and the board dimensions that admit tours that realize generators of the fundamental groups of each of the surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nullhomotopic and Generating Knight's Tours on Non-Orientable Surfaces Forrest, Bradley Lague, Zachary Combinatorics General Topology 05C45 (Primary) 57M15, 57M10, 57M05 (Secondary) We investigate closed knight's tours on Möbius strip and Klein bottle chess boards. In particular, we characterize the board dimensions that admit tours that are nullhomotopic and the board dimensions that admit tours that realize generators of the fundamental groups of each of the surfaces. |
| title | Nullhomotopic and Generating Knight's Tours on Non-Orientable Surfaces |
| topic | Combinatorics General Topology 05C45 (Primary) 57M15, 57M10, 57M05 (Secondary) |
| url | https://arxiv.org/abs/2406.05226 |