The occupation number constraints cannot be chosen freely. For example, if the total minimum exceeds the total number of electrons, k i=1 N min i > N or Ñ min k > N , no valid composition (and supergroup) exists. In chemical applications, the Pauli-principle enforces that the number of spin orbitals in a GAS space is larger than or equal to the minimum particle number. These "constraints of the constraints" have been discussed in the literature. We trivially note that if minima and maxima are the same in every GAS space, it is not possible to excite a particle from one GAS space to the other, and the spaces are disconnected. We also note that in the case of cumulative constraints it is possible to enforce tight inequalities for the last space Ñ min k = Ñ max k = N which tie the total number of particles and the GAS constraints together and allow shortcuts in an algorithm using cumulative constraints.