Bukh–Balla–Dräxler–Keevash–Sudakov conjecture on equiangular-line bounds

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Let r≥2r\geq2 be an integer. For α>0\alpha>0, let Nα(d)N_\alpha(d) denote the maximum number of equiangular lines in Rd\mathbb{R}^d with common absolute inner product α\alpha.

Bukh–Balla–Dräxler–Keevash–Sudakov conjecture. For sufficiently large nn,

N12r−1(d)=r(n−1)r−1+O(1).N_{\frac{1}{2r-1}}(d)=\frac{r(n-1)}{r-1}+O(1).

This conjecture proposes a general asymptotic formula for equiangular-line systems whose common angle is the reciprocal of an odd integer. The statement uses nn in its formula although the surrounding notation defines the parameter as dd; this notation mismatch should be checked against the source.

References

Primary source

Francesco Belardo, Sebastian M. Cioabă, Jack H. Koolen and Jianfeng Wang, “Open problems in the spectral theory of signed graphs”, arXiv:1907.04349 (2019).

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