  The role of the generalized Pauli constraints (GPCs) in higher spatial
dimensions and by incorporating spin degrees of freedom is systematically
explored for a system of interacting fermions confined by a harmonic trap.
Physical relevance of the GPCs is confirmed by analytical means for the ground
state in the regime of weak couplings by finding its vector of natural
occupation numbers close to the boundary of the allowed region. Such
quasipinning is found to become weaker in the intermediate and strong coupling
regime. The study of crossovers between different spatial dimensions by
detuning the harmonic trap frequencies suggests that quasipinning is
essentially an effect for systems with reduced spatial dimensionality. In
addition, we find that quasipinning becomes stronger by increasing the degree
of spin-polarization. Consequently, the number of states available around the
Fermi level plays a key role for the occurrence of quasipinning. This suggests
that quasipinning emerges from the conflict between energy minimization and
fermionic exchange symmetry.
