The partitioning introduced recently by Knowles [J. Chem. Phys. 156, 011101 (2022)] is analyzed and its connections with the Adams partitioning and the Davidson–Kapuy partitioning are discussed. Davidson’s partitioning is reformulated using the second quantized formalism. A relation is pointed out between the Knowles condition for the many-body perturbation theory zero order Hamiltonian and the CEPA0 equations.