论文标题
球形两距离集的光谱条件
Spectral conditions for spherical two-distance sets
论文作者
论文摘要
一组点$ s $在$ d $ d $ d $ d $ d $的欧几里得空间$ \ mathbb {r}^d $如果点之间的成对距离集具有基数二，则称为2距离集。如果2距离集的点位于$ \ mathbb {r}^{d} $中的单位球上，则称为球形。我们使用相关图的邻接矩阵和邻接矩阵的投影光谱在全部矢量的正交补体上表征球形2距离集。我们还确定了可以使用图形频谱来表示给定的球形二距离集的最低维空间。
A set of points $S$ in $d$-dimensional Euclidean space $\mathbb{R}^d$ is called a 2-distance set if the set of pairwise distances between the points has cardinality two. The 2-distance set is called spherical if its points lie on the unit sphere in $\mathbb{R}^{d}$. We characterize the spherical 2-distance sets using the spectrum of the adjacency matrix of an associated graph and the spectrum of the projection of the adjacency matrix onto the orthogonal complement of the all-ones vector. We also determine the lowest dimensional space in which a given spherical 2-distance set could be represented using the graph spectrum.
