Equiangular lines in low dimensional Euclidean spaces
We show that the maximum cardinality of an equiangular line system in 14 and 16 dimensions is 28 and 40, respectively, thereby solving a longstanding open problem. We also improve the upper bounds on the cardinality of equiangular line systems in 19 and 20 dimensions to 74 and 94, respectively.
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
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| Online Access: | https://hdl.handle.net/10356/152761 |
| _version_ | 1824457108755578880 |
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| author | Greaves, Gary Royden Watson Syatriadi, Jeven Yatsyna, Pavlo |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Greaves, Gary Royden Watson Syatriadi, Jeven Yatsyna, Pavlo |
| author_sort | Greaves, Gary Royden Watson |
| collection | NTU |
| description | We show that the maximum cardinality of an equiangular line system in 14 and 16 dimensions is 28 and 40, respectively, thereby solving a longstanding open problem. We also improve the upper bounds on the cardinality of equiangular line systems in 19 and 20 dimensions to 74 and 94, respectively. |
| first_indexed | 2025-02-19T04:04:45Z |
| format | Journal Article |
| id | ntu-10356/152761 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T04:04:45Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1527612021-12-11T11:06:32Z Equiangular lines in low dimensional Euclidean spaces Greaves, Gary Royden Watson Syatriadi, Jeven Yatsyna, Pavlo School of Physical and Mathematical Sciences Science::Mathematics::Discrete mathematics::Combinatorics Science::Mathematics::Discrete mathematics::Theory of computation Spherical Codes Equiangular We show that the maximum cardinality of an equiangular line system in 14 and 16 dimensions is 28 and 40, respectively, thereby solving a longstanding open problem. We also improve the upper bounds on the cardinality of equiangular line systems in 19 and 20 dimensions to 74 and 94, respectively. Ministry of Education (MOE) GRWG was supported by the Singapore Ministry of Education Academic Research Fund (Tier 1); grant numbers: RG29/18 and RG21/20. PY was supported by project PRIMUS/20/SCI/002 from Charles University 2021-12-11T11:06:32Z 2021-12-11T11:06:32Z 2021 Journal Article Greaves, G. R. W., Syatriadi, J. & Yatsyna, P. (2021). Equiangular lines in low dimensional Euclidean spaces. Combinatorica. https://dx.doi.org/10.1007/s00493-020-4523-0 0209-9683 https://hdl.handle.net/10356/152761 10.1007/s00493-020-4523-0 2-s2.0-85113999320 en RG29/18 RG21/20 Combinatorica © 2021 János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg. All rights reserved. |
| spellingShingle | Science::Mathematics::Discrete mathematics::Combinatorics Science::Mathematics::Discrete mathematics::Theory of computation Spherical Codes Equiangular Greaves, Gary Royden Watson Syatriadi, Jeven Yatsyna, Pavlo Equiangular lines in low dimensional Euclidean spaces |
| title | Equiangular lines in low dimensional Euclidean spaces |
| title_full | Equiangular lines in low dimensional Euclidean spaces |
| title_fullStr | Equiangular lines in low dimensional Euclidean spaces |
| title_full_unstemmed | Equiangular lines in low dimensional Euclidean spaces |
| title_short | Equiangular lines in low dimensional Euclidean spaces |
| title_sort | equiangular lines in low dimensional euclidean spaces |
| topic | Science::Mathematics::Discrete mathematics::Combinatorics Science::Mathematics::Discrete mathematics::Theory of computation Spherical Codes Equiangular |
| url | https://hdl.handle.net/10356/152761 |
| work_keys_str_mv | AT greavesgaryroydenwatson equiangularlinesinlowdimensionaleuclideanspaces AT syatriadijeven equiangularlinesinlowdimensionaleuclideanspaces AT yatsynapavlo equiangularlinesinlowdimensionaleuclideanspaces |