Equiangular lines in euclidean spaces: dimensions 17 and 18

We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem. Furthermore, by giving an explicit construction, we improve the lower bound on the maximum cardinality of an equiangular line system in 18 dimensions to 57

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Bibliographic Details
Main Authors:	Greaves, Gary Royden Watson, Syatriadi, Jeven, Yatsyna, Pavlo
Other Authors:	School of Physical and Mathematical Sciences
Format:	Article
Language:	English
Published:	2023
Subjects:	Science::Mathematics Equiangular Lines Dimensions 17 and 18
Online Access:	https://hdl.handle.net/10356/169357
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Institution:	Nanyang Technological University
Language:	English

id	sg-ntu-dr.10356-169357
record_format	dspace
spelling	sg-ntu-dr.10356-1693572023-07-17T15:34:55Z Equiangular lines in euclidean spaces: dimensions 17 and 18 Greaves, Gary Royden Watson Syatriadi, Jeven Yatsyna, Pavlo School of Physical and Mathematical Sciences Science::Mathematics Equiangular Lines Dimensions 17 and 18 We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem. Furthermore, by giving an explicit construction, we improve the lower bound on the maximum cardinality of an equiangular line system in 18 dimensions to 57 Ministry of Education (MOE) Submitted/Accepted version The first author was supported in part by the Singapore Ministry of Education Academic Research Fund (Tier 1); grant numbers: RG29/18 and RG21/20. The third author was supported in part by the project PRIMUS/20/SCI/002 from Charles University. 2023-07-14T06:44:02Z 2023-07-14T06:44:02Z 2023 Journal Article Greaves, G. R. W., Syatriadi, J. & Yatsyna, P. (2023). Equiangular lines in euclidean spaces: dimensions 17 and 18. Mathematics of Computation, 92(342), 1867-1903. https://dx.doi.org/10.1090/mcom/3832 0025-5718 https://hdl.handle.net/10356/169357 10.1090/mcom/3832 2-s2.0-85152642965 342 92 1867 1903 en RG29/18 RG21/20 Mathematics of Computation © 2023 American Mathematical Society. All rights reserved. This paper was published in Mathematics of Computation and is made available with permission of American Mathematical Society. application/pdf
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 Dimensions 17 and 18
spellingShingle	Science::Mathematics Equiangular Lines Dimensions 17 and 18 Greaves, Gary Royden Watson Syatriadi, Jeven Yatsyna, Pavlo Equiangular lines in euclidean spaces: dimensions 17 and 18
description	We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem. Furthermore, by giving an explicit construction, we improve the lower bound on the maximum cardinality of an equiangular line system in 18 dimensions to 57
author2	School of Physical and Mathematical Sciences
author_facet	School of Physical and Mathematical Sciences Greaves, Gary Royden Watson Syatriadi, Jeven Yatsyna, Pavlo
format	Article
author	Greaves, Gary Royden Watson Syatriadi, Jeven Yatsyna, Pavlo
author_sort	Greaves, Gary Royden Watson
title	Equiangular lines in euclidean spaces: dimensions 17 and 18
title_short	Equiangular lines in euclidean spaces: dimensions 17 and 18
title_full	Equiangular lines in euclidean spaces: dimensions 17 and 18
title_fullStr	Equiangular lines in euclidean spaces: dimensions 17 and 18
title_full_unstemmed	Equiangular lines in euclidean spaces: dimensions 17 and 18
title_sort	equiangular lines in euclidean spaces: dimensions 17 and 18
publishDate	2023
url	https://hdl.handle.net/10356/169357
_version_	1773551406609858560

Equiangular lines in euclidean spaces: dimensions 17 and 18

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