  The atomic cluster expansion (ACE) has been highly successful for the
parameterisation of symmetric (invariant or equivariant) properties of
many-particle systems. Here, we generalize its derivation to anti-symmetric
functions. We show how numerous well-known linear representations of wave
functions naturally arise within this framework and we explore how recent
successful nonlinear parameterisations can be further enhanced by employing ACE
methodology. From this analysis we propose a wide design space of promising
wave function representations.
