论文标题
关于模型集中的算术进展
On arithmetic progressions in model sets
论文作者
论文摘要
在这个项目中，我们显示了模型集中的任意长度算术进程的存在，而欧几里得$ d $ -space中的迈耶集则存在。我们证明了Meyer套装的Van der Waerden类型定理。我们表明，Meyer集的纯点子集具有正密度，并且纯点衍射包含任意长度的算术进程。
In this project we show the existence of arbitrary length arithmetic progressions in model sets and Meyer sets in the Euclidean $d$-space. We prove a van der Waerden type theorem for Meyer sets. We show that pure point subsets of Meyer sets with positive density and pure point diffraction contain arithmetic progressions of arbitrary length.
