Classification of equiangular lines with fixed angle $\arccos(1/(1+2\sqrt2))$
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912938924703744 |
|---|---|
| author | Gossett, Theodore Jiang, Zilin Teets, Adam Wellner, Zoe |
| author_facet | Gossett, Theodore Jiang, Zilin Teets, Adam Wellner, Zoe |
| contents | We determine the maximum number $N_α(d)$ of equiangular lines with fixed angle $\arccosα$ for $α= 1/(1+2\sqrt2)$ in $d$-dimensional Euclidean space: $2,3,4,6,8,10,14,15,16,17,18,20,22$ for $d \in \{2,\dots,14\}$, and $\max(24, \lfloor 3(d-1)/2 \rfloor)$ for $d \ge 15$. This appears to be the first complete determination of $N_α(d)$ in all dimensions $d$ for a fixed nontrivial $α$, since the work of Lemmens and Seidel for $α= 1/3$ in 1973. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02469 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of equiangular lines with fixed angle $\arccos(1/(1+2\sqrt2))$ Gossett, Theodore Jiang, Zilin Teets, Adam Wellner, Zoe Combinatorics Metric Geometry 05C50, 52C35 We determine the maximum number $N_α(d)$ of equiangular lines with fixed angle $\arccosα$ for $α= 1/(1+2\sqrt2)$ in $d$-dimensional Euclidean space: $2,3,4,6,8,10,14,15,16,17,18,20,22$ for $d \in \{2,\dots,14\}$, and $\max(24, \lfloor 3(d-1)/2 \rfloor)$ for $d \ge 15$. This appears to be the first complete determination of $N_α(d)$ in all dimensions $d$ for a fixed nontrivial $α$, since the work of Lemmens and Seidel for $α= 1/3$ in 1973. |
| title | Classification of equiangular lines with fixed angle $\arccos(1/(1+2\sqrt2))$ |
| topic | Combinatorics Metric Geometry 05C50, 52C35 |
| url | https://arxiv.org/abs/2603.02469 |