The number of inter-space excitations are limited by constraining the particle number per GAS space. In the original work on the GAS approach 27,63-65 the word supergroup was utilized to refer to a given distribution of particles (α-, β-, or in general electrons) among GAS subspaces, while fullfilling the GAS constraints. We will interpret supergroups as a special case of compositions, a term borrowed from number theory. A composition is a solution to the following integer equation