Puiseux series about exceptional singularities dictated by symmetry-allowed Hessenberg forms of perturbation matrices
The research uses Puiseux series to study exceptional singularities (EPns) in non-Hermitian systems by analyzing symmetry-allowed perturbations represented as upper-k Hessenberg forms. It shows that P and C symmetries limit EP3 splitting to $\sim \epsilon_1/2$, while PT symmetry allows for the stronger $\sim \epsilon_1/3$ singularity. This framework helps design sensors based on these singularities.