Relations between N-representable n-particle densities

We show that the convex set that determines which n-particle densities can arise from an N-particle wavefunction becomes smaller when N increases. We also show that their boundaries have empty intersection for fermions (but not for bosons). The N-representability conditions thus become more constraining for more particles. Finally, we show that it is impossible, in a combinatorial way, to determine a unique n-particle density that integrates to a given m-particle density (where m < n).