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Given a monic degree $n$ polynomial $f(z)$ with no double roots, and a phase $0\leq \theta < \pi$, there are natural constructions which associate to this data: a noncrossing matching on $2n$ ...

Consider the polynomial set: $$ f_{ij} = (t_i - t_j)x_i x_j + x_i - x_j, \quad (1 \leq j < i \leq 2n) $$ where $ t_1, t_2, \dots, t_{2n} $ are pairwise distinct. Let's look at the non-crossing ...