Periodicity and decidability of tilings of ℤ2

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-01-23 DOI:10.1353/ajm.2020.0006

S. Bhattacharya

引用次数: 24

Abstract

abstract:We prove that any finite set $F\subset{\Bbb Z}^2$ that tiles ${\Bbb Z}^2$ by translations also admits a periodic tiling. As a consequence, the problem whether a given finite set $F$ tiles ${\Bbb Z}^2$ is decidable.

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tilings的周期性和可判定性ℤ2.

文摘：我们证明了任何有限集$F\subet｛\bbZ｝^2$通过翻译平铺$｛\bb Z｝^ 2$也允许周期平铺。因此，给定的有限集$F$瓦片$｛\bbZ｝^2$是否是可判定的问题。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.