论文标题
点包装的相似性异构体
Similarity Isometries of Point Packings
论文作者
论文摘要
$ \ mathbb {r}^d $的线性等距$ r $称为晶格$γ\ subseteq \ mathbb {r}^d $的相似等轴测图，如果存在正真实数字$β$，则$βRγ$是$βRγ$的（finite Index Index Index in）$γ$。集合$βRγ$被称为$γ$的类似sublattice。晶格$γ$产生的（晶体学）点堆积是$γ$的结合，有限的许多转移副本为$γ$。在这项研究中，相似性等法的概念扩展到点包装。我们为点包装的相似性等法提供了表征，并确定相应的相似子包。将讨论平面示例，即$ 1 \ times 2 $矩形晶格和六角形包装（或蜂窝晶格）。最后，我们还考虑了通过研究移位点堆积的相似性异构体来考虑与原点不同的点包装的相似性等法。特别是，将计算一定移动的六角形填料的相似性等法，并将其与六角形填料进行比较。
A linear isometry $R$ of $\mathbb{R}^d$ is called a similarity isometry of a lattice $Γ\subseteq \mathbb{R}^d$ if there exists a positive real number $β$ such that $βRΓ$ is a sublattice of (finite index in) $Γ$. The set $βRΓ$ is referred to as a similar sublattice of $Γ$. A (crystallographic) point packing generated by a lattice $Γ$ is a union of $Γ$ with finitely many shifted copies of $Γ$. In this study, the notion of similarity isometries is extended to point packings. We provide a characterization for the similarity isometries of point packings and identify the corresponding similar subpackings. Planar examples will be discussed, namely, the $1 \times 2$ rectangular lattice and the hexagonal packing (or honeycomb lattice). Finally, we also consider similarity isometries of point packings about points different from the origin by studying similarity isometries of shifted point packings. In particular, similarity isometries of a certain shifted hexagonal packing will be computed and compared with that of the hexagonal packing.
