Toroidal Hitomezashi Patterns
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929209361825792 |
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| author | Ren, Qiuyu Zhang, Shengtong |
| author_facet | Ren, Qiuyu Zhang, Shengtong |
| contents | Extending a proposal of Defant and Kravitz [Discrete Mathematics, \textbf{1}, 347 (2024)], we define Hitomezashi patterns and loops on a torus and provide several structural results for such loops. For a given pattern, our main theorems give optimal residual information regarding the Hitomezashi loop length, loop count, as well as possible homology classes of such loops. Special attention is paid to toroidal Hitomezashi patterns that are symmetric with respect to the diagonal $x = y$, where we establish a novel connection between Hitomezashi and knot theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02741 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Toroidal Hitomezashi Patterns Ren, Qiuyu Zhang, Shengtong Combinatorics General Topology 00A08, 00A66, 05B50 Extending a proposal of Defant and Kravitz [Discrete Mathematics, \textbf{1}, 347 (2024)], we define Hitomezashi patterns and loops on a torus and provide several structural results for such loops. For a given pattern, our main theorems give optimal residual information regarding the Hitomezashi loop length, loop count, as well as possible homology classes of such loops. Special attention is paid to toroidal Hitomezashi patterns that are symmetric with respect to the diagonal $x = y$, where we establish a novel connection between Hitomezashi and knot theory. |
| title | Toroidal Hitomezashi Patterns |
| topic | Combinatorics General Topology 00A08, 00A66, 05B50 |
| url | https://arxiv.org/abs/2309.02741 |