Extending the methods of Metrebian (2018), we prove that punctured intervals tile ${\mathbb{Z}}^3$. This solves two questions of Metrebian and completely resolves a question of Gruslys, Leader and Tan. We also pose a question that asks whether there is a relation between the genus g (number of holes) in a one‐dimensional tile T and a uniform bound d such that T tiles ${\mathbb{Z}}^d$. An affirmative answer would generalize a conjecture of Gruslys, Leader and Tan (2016).

中文翻译：

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间隔间隔标题Z3

扩展了Metrebian（2018）的方法，我们证明了打孔间隔平铺 ${\mathbb{ž}}^3$。这解决了Metrebian的两个问题，并彻底解决了Gruslys，Leader和Tan的问题。我们还提出一个问题，询问一维瓦片T的属g（孔数）与均匀边界d之间是否存在关系，使得T瓦片${\mathbb{ž}}^d$。肯定的回答将概括出Gruslys，Leader和Tan（2016）的猜想。