Symbolic Computations of the Two-Colored Diagrams for Central Configurations of the Planar N-vortex Problem

We apply the singular sequence method to investigate the finiteness problem for stationary configurations of the planar N-vortex problem. The initial step of the singular sequence method involves identifying all two-colored diagrams. These diagrams represent potential scenarios where finiteness may fail. We develop a symbolic computation algorithm to determine all two-colored diagrams for central configurations of the planar N-vortex problem.