Abstract
We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem.
| Original language | English |
|---|---|
| Pages (from-to) | 1867-1903 |
| Number of pages | 37 |
| Journal | Mathematics of Computation |
| Volume | 92 |
| Issue number | 342 |
| DOIs | |
| Publication status | Published - 8 Mar 2023 |
| MoE publication type | A1 Journal article-refereed |
Funding
Received by the editor July 29, 2021, and, in revised form, May 17, 2022, September 11, 2022, January 4, 2023, and January 16, 2023. 2020 Mathematics Subject Classification. Primary 05B40; Secondary 05B20. Key words and phrases. Equiangular lines, dimensions 17 and 18, compatible polynomials, eigenspace angles, polynomial interlacing. 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.
Keywords
- compatible polynomials
- dimensions 17 and 18
- eigenspace angles
- Equiangular lines
- polynomial interlacing