Let's constrain the active-space, by introducing vector ξ p (Boolean vector, True : part of active-space, False : not part of active-space) xor ξ z (array enumerating active orbitals). The FCI combinatorics then may be applied within the occupied active-orbitals going to the vacant active-orbitals, this yields a set of {Λ ↑ ξ , Λ ↓ ξ }. These occupation values may be recast into the proper orbitals by the composition operation: