{"title":"Toroidal Hitomezashi patterns","authors":"Qiuyu Ren , Shengtong Zhang","doi":"10.1016/j.disc.2024.114231","DOIUrl":null,"url":null,"abstract":"<div><p>Extending a proposal of Defant and Kravitz (2024) <span><span>[2]</span></span>, 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 <span><math><mi>x</mi><mo>=</mo><mi>y</mi></math></span>, where we establish a novel connection between Hitomezashi and knot theory.</p></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 1","pages":"Article 114231"},"PeriodicalIF":0.7000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0012365X24003625/pdfft?md5=8878c11c7ff09a39b29f9d80243aab95&pid=1-s2.0-S0012365X24003625-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24003625","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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 , where we establish a novel connection between Hitomezashi and knot theory.
期刊介绍：
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
