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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/170924 |
| _version_ | 1811697314607136768 |
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| author | Greaves, Gary Royden Watson Syatriadi, Jeven |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Greaves, Gary Royden Watson Syatriadi, Jeven |
| author_sort | Greaves, Gary Royden Watson |
| collection | NTU |
| description | 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
$(x-22)(x-2)^{42} (x+6)^{15} (x+8)^2$. |
| first_indexed | 2024-10-01T07:53:18Z |
| format | Journal Article |
| id | ntu-10356/170924 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:53:18Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1709242023-10-09T02:03:27Z Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs Greaves, Gary Royden Watson Syatriadi, Jeven School of Physical and Mathematical Sciences Science::Mathematics Equiangular Lines Jacobi Identity 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 $(x-22)(x-2)^{42} (x+6)^{15} (x+8)^2$. Ministry of Education (MOE) The first author was supported by the Singapore Ministry of Education Academic Research Fund (Tier 1); grant numbers: RG21/20 and RG23/20. 2023-10-09T01:58:39Z 2023-10-09T01:58:39Z 2024 Journal Article Greaves, G. R. W. & Syatriadi, J. (2024). Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs. Journal of Combinatorial Theory, Series A, 201, 105812-. https://dx.doi.org/10.1016/j.jcta.2023.105812 0097-3165 https://hdl.handle.net/10356/170924 10.1016/j.jcta.2023.105812 2-s2.0-85171550754 201 105812 en RG21/20 RG23/20. Journal of Combinatorial Theory, Series A © 2023 Elsevier Inc. All rights reserved. |
| spellingShingle | Science::Mathematics Equiangular Lines Jacobi Identity Greaves, Gary Royden Watson Syatriadi, Jeven Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs |
| title | Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs |
| title_full | Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs |
| title_fullStr | Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs |
| title_full_unstemmed | Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs |
| title_short | Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs |
| title_sort | real equiangular lines in dimension 18 and the jacobi identity for complementary subgraphs |
| topic | Science::Mathematics Equiangular Lines Jacobi Identity |
| url | https://hdl.handle.net/10356/170924 |
| work_keys_str_mv | AT greavesgaryroydenwatson realequiangularlinesindimension18andthejacobiidentityforcomplementarysubgraphs AT syatriadijeven realequiangularlinesindimension18andthejacobiidentityforcomplementarysubgraphs |