解决瓷砖上的七个半问题

IF 0.7 4区数学 Q2 MATHEMATICS

Electronic Journal of Combinatorics Pub Date : 2023-06-30 DOI:10.37236/11813

Bojan Bašić, Aleksa Džuklevski, Anna Slivková

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引用次数: 0

摘要

关于拼贴的四个问题，与所谓的Heesch数、等面数、m -形态图和σ -形态图有关，可以在拼贴概念的四种变体中提出:具有更多元素的原集、不相连的砖块、彩色砖块和更大维度空间中的镶嵌。总共有16种组合。其中五个已经在文献中解决，一个已经部分解决。我们在这里解出了剩下的7个组合，并完成了部分解。

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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Solutions to Seven and a Half Problems on Tilings

Four problems about tilings, related to the so-called: Heesch number, isohedral number, $m$-morphic figures, and $\sigma$-morphic figures, can be asked in four variations of the notion of tiling: protosets with more elements, disconnected tiles, colored tiles and tessellations in larger-dimensional spaces. That makes $16$ combinations in total. Five among them have been previously solved in the literature, and one has been partially solved. We here solve seven of the remaining combinations, and additionally complete that partial solution.

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来源期刊

Electronic Journal of Combinatorics 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

212

审稿时长

3-6 weeks

期刊介绍： The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.