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

Abstract

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 $(x-22)(x-2{)}^{42}(x+6{)}^{15}(x+8{)}^2$.

26 pages. Updated to match the published, journal version

References in corpus (1)

• A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices

Cited by in corpus (1)

• Sets of equiangular lines in dimension $18$ constructed from $A_9\oplus A_9\oplus A_1$