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 $\mathbb R^{18}$ 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: Greaves, Gary Royden Watson, Syatriadi, Jeven
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2023
Subjects:
Science::Mathematics
Equiangular Lines
Jacobi Identity
Online Access:https://hdl.handle.net/10356/170924
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Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-170924
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spelling sg-ntu-dr.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.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Equiangular Lines
Jacobi Identity
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
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 $(x-22)(x-2)^{42} (x+6)^{15} (x+8)^2$.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Greaves, Gary Royden Watson
Syatriadi, Jeven
format Article
author Greaves, Gary Royden Watson
Syatriadi, Jeven
author_sort Greaves, Gary Royden Watson
title 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_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_sort real equiangular lines in dimension 18 and the jacobi identity for complementary subgraphs
publishDate 2023
url https://hdl.handle.net/10356/170924
_version_ 1781793868722733056

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