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Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs
- Source :
- Journal of Combinatorial Theory, Series A, Volume 201, January 2024, 105812
- Publication Year :
- 2022
-
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 $(x-22)(x-2)^{42} (x+6)^{15} (x+8)^2$.<br />Comment: 26 pages. Updated to match the published, journal version
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Combinatorial Theory, Series A, Volume 201, January 2024, 105812
- Publication Type :
- Report
- Accession number :
- edsarx.2206.04267
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jcta.2023.105812