Diagram technique for a two-dimensional system of interacting electrons in a strong magnetic field

The peculiarities of the diagram technique for a two-dimensional polarized system of interacting particles in a magnetic field are investigated. It is assumed that interaction does not cause transitions between the Landau levels. It is shown that in each order of perturbation theory topologically different diagrams constitute separate groups. Inside each group all diagrams are equal. A principle is formulated according to which the diagrams are divided into separate groups and a number of diagrams in the group is found. A class of diagrams equivalent to an electron-hole interaction is determined, the summation of which gives rise to a singularity in a scattering amplitude corresponding to a charge-density-wave instability.