  How best to think about quantum systems under permutation invariance is a
question that has received a great deal of attention in the literature. But
very little attention has been paid to taking seriously the proposal that
permutation invariance reflects a representational redundancy in the formalism.
Under such a proposal, it is far from obvious how a constituent quantum system
is represented. Consequently, it is also far from obvious how quantum systems
compose to form assemblies, i.e. what is the formal structure of their
relations of parthood, overlap and fusion.
  In this paper, I explore one proposal for the case of fermions and their
assemblies. According to this proposal, fermionic assemblies which are not
entangled -- in some heterodox, but natural sense of 'entangled' -- provide a
prima facie counterexample to classical mereology. This result is puzzling;
but, I argue, no more intolerable than any other available interpretative
option.
