Faddeev-Yakubovsky 3-body decomposition; Cayley n^{n-2} spanning trees

Faddeev-Yakubovsky 3-body decomposition framework (Faddeev 1961 Sov Phys JETP 12, 1014; Yakubovsky 1967 Sov J Nucl Phys 5, 937). Setup: the 3-body Schroedinger equation with pairwise potentials V = V_{12} + V_{13} + V_{23} is decomposed…