Periodicity and decidability of tilings of ℤ2

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics 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

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.