  We present generalized versions of the concepts of seniority number and
ionicity. These generalized numbers count respectively the partially occupied
and fully occupied shells for any partition of the orbital space into shells.
The Hermitian operators whose eigenspaces correspond to wave functions of
definite generalized seniority or ionicity values are introduced. The
generalized seniority numbers (GSNs) afford to establish refined hierarchies of
configuration interaction (CI) spaces within those of fixed ordinary seniority.
Such a hierarchy is illustrated on the buckminsterfullerene molecule.
