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 $\mathbb R^{18}$ 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 pol...
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| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/170924 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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
$(x-22)(x-2)^{42} (x+6)^{15} (x+8)^2$. |
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