2023/09/06 by Qiuyu Ren, Shengtong Zhang, Ren, Qiuyu +1 · 1 citation
Mathematics · #00A08 #00A66 #05B50 #Combinatorics (math.CO) #FOS: Mathematics #General Topology (math.GN) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2309.02741
openalex publication_date 2023/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Extending a proposal of Defant and Kravitz [Discrete Mathematics, 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.