Toroidal Hitomezashi patterns

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-08-30 DOI:10.1016/j.disc.2024.114231

Qiuyu Ren , Shengtong Zhang

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 $x = y$ , where we establish a novel connection between Hitomezashi and knot theory.

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环状人字形图案

我们扩展了德凡特和克拉维茨（Defant and Kravitz，2024 年）[2] 的提议，定义了环上的 Hitomezashi 图案和环，并提供了此类环的若干结构性结果。对于给定的模式，我们的主要定理给出了有关常陆环长、环数以及此类环可能的同构类的最优残差信息。我们特别关注相对于对角线 x=y 对称的环状人字桥图案，在此我们建立了人字桥与结理论之间的新联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

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.