Papers › Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs
Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs
Gary R. W. Greaves, Jeven Syatriadi
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We show that the maximum cardinality of an equiangular line system in ℝ¹⁸ 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.
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