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

TL;DR

This paper introduces a symbolic computation algorithm to identify all two-colored diagrams in the planar N-vortex problem, aiding the investigation of the finiteness of stationary configurations using the singular sequence method.

Contribution

The paper develops a novel symbolic computation approach to systematically find all relevant two-colored diagrams for central configurations in the N-vortex problem.

Findings

Successfully identified all two-colored diagrams for given configurations.

Enhanced understanding of potential finiteness failures in vortex configurations.

Provided a computational tool for further analysis of vortex dynamics.

Abstract

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.