论文标题
用两种尺寸的高管填充空间 - 毕达哥拉斯的瓷砖较高的尺寸
Filling space with hypercubes of two sizes -- The pythagorean tiling in higher dimensions
论文作者
论文摘要
我们将$ \ mathbb {r}^n $的单方面晶格瓷砖构建到两个不同的侧面长度$ p $或$ q $的超级底盘中。这将毕达哥拉斯的平铺概括为$ \ mathbb {r}^2 $。我们还表明，这个瓷砖是独一无二的对称性的，这证明了Bölcskei与2001年的猜想变化。对于正整数，此瓷砖也提供了$（\ Mathbb {z}}/（p^n+q^n+q^n）\ mathbb {z} {z}）的瓷砖。
We construct a unilateral lattice tiling of $\mathbb{R}^n$ into hypercubes of two differnet side lengths $p$ or $q$. This generalizes the Pythagorean tiling in $\mathbb{R}^2$. We also show that this tiling is unique up to symmetries, which proves a variation of a conjecture by Bölcskei from 2001. For positive integers $p$ and $q$ this tiling also provides a tiling of $(\mathbb{Z}/(p^n+q^n)\mathbb{Z})^n$.
