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

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...

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Veröffentlicht in:Journal of combinatorial theory. Series A 2024-01, Vol.201, p.105812, Article 105812
Hauptverfasser: Greaves, Gary R.W., Syatriadi, Jeven
Format: Artikel
Sprache:eng
Schlagworte:
Equiangular lines
Four eigenvalues
Graphs
Jacobi identity
Seidel matrix
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Zusammenfassung: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.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2023.105812