It is rather difficult to write a closed expression for the scaling of n sg with respect to the number of particles, N , GAS spaces, n GAS , and GAS constraints. It has to be stressed that the number of supergroups is independent from the number of orbitals and in the best case of purely disconnected spaces there is only one supergroup, regardless of N and n GAS . In the worst case of no miminum or maximum restrictions, the scaling of n sg is combinatorial and given by the number of compositions (Lemma 6.4) as