Toroidal Hitomezashi patterns

Extending a proposal of Defant and Kravitz (2024) [2], 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 pos...

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Bibliographic Details
Published inDiscrete mathematics Vol. 348; no. 1; p. 114231
Main Authors Ren, Qiuyu, Zhang, Shengtong
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2025
Subjects
Hitomezashi
Knot
Stitching
Hitomezashi
Stitching
Knot
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Summary:Extending a proposal of Defant and Kravitz (2024) [2], 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.
ISSN:0012-365X
DOI:10.1016/j.disc.2024.114231