论文标题
维度18中的真实等线线和互补子图的雅各比身份
Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs
论文作者
论文摘要
我们表明，$ \ Mathbb r^{18} $中的等态线系统的最大基数最多是$ 59 $。我们的证明包括雅各比身份的新应用用于互补子图。特别是，我们表明，不存在其邻接矩阵具有特征性多项式$（x-22）（x-2）（x-2）^{42}（x+6）^{15}（x+8）^2 $的图。
We show that the maximum cardinality of an equiangular line system in $\mathbb R^{18}$ is at most $59$. Our proof includes a novel application of the Jacobi identity for complementary subgraphs. In particular, we show that there does not exist a graph whose adjacency matrix has characteristic polynomial $(x-22)(x-2)^{42} (x+6)^{15} (x+8)^2$.
