We consider two compositions to be different, if their order differs, i.e. 2+1 = 3 and 1+2 = 3 are two different compositions. If we identify the number of summands k with the number of GAS spaces, N with the total number of particles, and x i with the number of particles in the i-th GAS space, we can easily interpret a given composition as distribution of particles over GAS spaces. We can constrain the allowed compositions, hence the allowed interspace excitations, by defining local or cumulative minimum and maximum occupation numbers per GAS space. We write N min i , N max i for local constraints and Ñ min i , Ñ max i for cumulative constraints. GAS allowed compositions are then those for which ∀i,