论文标题
在$（\ mathbb {z} _p）^d $中的瓷砖和虚弱的瓷砖
Tiling and weak tiling in $(\mathbb{Z}_p)^d$
论文作者
论文摘要
我们讨论有限的阿贝尔群体中平铺，薄层和频谱集的关系。特别是，在小学$ p $ -groups $（\ mathbb {z} _p）^d $中，我们引入了一个平均过程，该过程导致了自然研究对象：一个四翼函数，可以被视为瓷砖和光谱集的常见概括。我们以$ d = 1、2 $的形式表征了这样的4个tuply，并证明了$ d = 3 $的部分结果。
We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary $p$-groups $(\mathbb{Z}_p)^d$, we introduce an averaging procedure that leads to a natural object of study: a 4-tuple of functions which can be regarded as a common generalization of tiles and spectral sets. We characterize such 4-tuples for $d=1, 2$, and prove some partial results for $d=3$.
