Polynomial Method for Constructing Equilibrium Configurations of Point Vortices in the Plane

The problem of constructing and classifying stationary and translating configurations of point vortices with an arbitrary choice of circulations is studied. The polynomial method enabling one to find any such configuration is described in detail. Stationary configurations for vortex systems with circulations $\Gamma$, $-\mu\Gamma$ are classified in the case of integer $\mu$. New configurations are obtained.