Tiling with sets of polyominoes

Solomon W. Golomb
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引用次数: 71

Abstract

The definitions and lattice hierarchy previously established for tiling regions with individual polyominoes are extended to finite sets of polyominoes. The problem of tiling the infinite plane with replicas of a finite set of polyominoes is proved to be logically equivalent to Wang's “domino problem,” which is known to be algorithmically undecidable. Several different ways of extending the notion of rep-tility from single polyominoes to sets of polyominoes are discussed. Some related results of Ikeno regarding tiling with polyiamonds (shapes composed of equilateral triangles) are mentioned.

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用一组多项式平铺
将先前建立的具有单个多项式的平铺区域的定义和晶格层次扩展到有限多项式集。用有限多诺骨牌的复制品在无限平面上平铺的问题被证明在逻辑上等同于王的“多米诺骨牌问题”,这是已知的算法上不可判定的。讨论了将可重复性的概念从单个多多项式扩展到多多项式集的几种不同方法。提到了池野关于用多边形(由等边三角形组成的形状)平铺的一些相关结果。
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