Sums of squares of many-particle matrix elements over all the quantum numbers except seniority numbers are directly related to two-particle matrix elements of a particle-particle interaction and of the corresponding particle-hole interaction.
The seniority scheme introduced by Racah is generalized in the case of degenerate levels. Many formulae for the pure configuration j n are modified in order to calculate matrix elements in this generalized seniority scheme. It is especially the most interesting result that the diagonal matrix element of two-body operators between the states with the same seniority v can be expressed in terms of the matrix elements in the v -particle system. This result, of course, holds in the case of the pure configuration.