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
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2023
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| Online Access: | https://hdl.handle.net/10356/169357 |
| _version_ | 1824453753276727296 |
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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 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 |
| first_indexed | 2025-02-19T03:11:25Z |
| format | Journal Article |
| id | ntu-10356/169357 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:11:25Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-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 |
| 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 |
| title | 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_short | Equiangular lines in euclidean spaces: dimensions 17 and 18 |
| title_sort | equiangular lines in euclidean spaces dimensions 17 and 18 |
| topic | Science::Mathematics Equiangular Lines Dimensions 17 and 18 |
| url | https://hdl.handle.net/10356/169357 |
| work_keys_str_mv | AT greavesgaryroydenwatson equiangularlinesineuclideanspacesdimensions17and18 AT syatriadijeven equiangularlinesineuclideanspacesdimensions17and18 AT yatsynapavlo equiangularlinesineuclideanspacesdimensions17and18 |