论文标题
cowEight晶格$ a^*_ n $和晶格简单
Coweight lattice $A^*_n$ and lattice simplices
论文作者
论文摘要
在静电测量中存在许多六角形晶格的索引-K $ sublattices，因为存在具有归一化体积$ k $的晶格三角形，直至单型等效，可以使用orbifolds来解释。在维度3中，注意到FCC和BCC晶格的sublattices数量以及四面体的晶格数量似乎都是相同的。我们在CowEight Lattice $ a^*_ n $和$ n $二维晶格简上的转子之间提供了两次射击。它解释，证明并概括了观察到的任意维度的巧合。
There exist as many index-$k$ sublattices of the hexagonal lattice up to isometry as there exist lattice triangles with normalized volume $k$ up to unimodular equivalence, which can be explained using orbifolds. In dimension 3, it was noted that the number of sublattices of the fcc and the bcc lattices and the number of lattice tetrahedra all seem to be the same. We provide a bijection between the sublattices of the coweight lattice $A^*_n$ and the $n$-dimensional lattice simplices. It explains, proves, and generalizes the observed coincidences to arbitrary dimension.
