Crossing-Symmetric Reduction Equations for Dressed Vertices

We study the topological structure of vertex functions classified by their external points n and minimum number of intermediate-state particles i. We introduce a scheme of topological classifications according to the channels or partitions in which the intermediate states appear and show how to avoid overcounting. We demonstrate how to construct equations relating each class to the others and forming a crossing-symmetric generalization of the Landau-Migdal and Bethe-Salpeter rescattering equations.