In GAS the active orbitals are partitioned into a number of active subspaces. Then only some distributions of particles among these subspaces are allowed, for example by defining a minimum and maximum particle number per GAS space. A given allowed distribution of particles among the subspaces is called a supergroup. For a given supergroup all possible configurations inside each subspace are allowed, i.e. a full CI wave function inside each subspace is generated. If there is only one supergroup the GAS spaces are disconnected and no excitations between them are allowed. In Figure a possible GAS wave function is displayed. The GAS algorithm is a natural generalization of other truncated FCI schemes and it can easily be used to construct restricted active spaces (RAS) (three subspaces) or complete active spaces (CAS) wave function expansions. As we showed in our previous work operation). Counting how many particles an excitation transfers between GAS spaces is a trivial operation. Hence, for a given supergroup (and all determinants belonging to it), an excitation is GAS allowed if the resulting particle distribution is still inside the chosen GAS constraints. This implies in particular that the starting determinant |D i is not necessary, only its supergroup is required to determine if an excitation is GAS allowed.