Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs

• Main Authors: Greaves, Gary Royden Watson, Syatriadi, Jeven
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2023
• Subjects: Science::Mathematics; Equiangular Lines; Jacobi Identity
• Online Access: https://hdl.handle.net/10356/170924
• Institution: Nanyang Technological University

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 pol...