论文标题
周期序列的密度函数
Density functions of periodic sequences
论文作者
论文摘要
周期点设置所有固体结晶材料的模型，其结构以刚性形式确定，应研究以保持刚性运动或保持点间距离的等轴测图。在2021年H.Edelsbrunner等。引入了无限函数的无限序列，这些函数是周期性集合的连续等轴测不变。这些密度函数即使在线中的点序列的周期序列中，这些密度函数也是高度不平凡的。本文充分描述了任何周期序列及其对称性的密度函数。从理论上讲，显式描述证实了以前仅通过有限样本计算的密度函数的一致性。
Periodic point sets model all solid crystalline materials whose structures are determined in a rigid form and should be studied up to rigid motion or isometry preserving inter-point distances. In 2021 H.Edelsbrunner et al. introduced an infinite sequence of density functions that are continuous isometry invariants of periodic point sets. These density functions turned out to be highly non-trivial even in dimension 1 for periodic sequences of points in the line. This paper fully describes the density functions of any periodic sequence and their symmetry properties. The explicit description theoretically confirms coincidences of density functions that were previously computed only through finite samples.
