5 papers · 1 filter
New bounds for equiangular lines and Balla's conjecture
Chuanyuan Ge, Shiping Liu
Let denote the maximum number of equiangular lines in with common angle . Balla conjectured that, if the spectral radius order $κ_{\frac{1-α}{2α…
A new proof of the Lemmens-Seidel conjecture
Chuanyuan Ge, Shiping Liu
In this paper, we give a new proof of the Lemmens-Seidel conjecture on the maximum number of equiangular lines with a common angle . This conjecture was previously re…
On finiteness of spectral radius order
Yanlong Ding, Chuanyuan Ge, Shiping Liu
The concept of spectral radius order plays an crucial role in the breakthrough work on equiangular lines due to Jiang, Tidor, Yao, Zhang, and Zhao [Ann. of Math. (2) 194 (2021), no…
Equiangular lines via nodal domains
Chuanyuan Ge, Shiping Liu
For given and , we show that the maximum multiplicity that can appear as the second largest eigenvalue of a connected graph with maximum degree at most $Δ…
Spectral bounds of multi-way Cheeger constants via cyclomatic number
Chuanyuan Ge
As a non-trivial extension of the celebrated Cheeger inequality, the higher-order Cheeger inequalities for graphs due to Lee, Oveis Gharan and Trevisan provide for each an uppe…