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

We show that the maximum cardinality of an equiangular line system in 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. [ABSTRACT FROM AUTHOR]