  Several distinct classes of unitary mode transformations have been known to
exhibit the strict suppression of a large set of transmission events, as a
consequence of totally destructive many-particle interference. In another work
[Dittel et al., Phys. Rev. Lett. 120, 240404 (2018)] we unite these cases by
identifying a general class of unitary matrices which exhibit such
interferences. Here, we provide a detailed theoretical analysis that
substantially expands on all aspects of this generalisation: We prove the
suppression laws put forward in our other paper, establish how they interrelate
with forbidden single-particle transitions, show how all suppression laws
hitherto known can be retrieved from our general formalism, and discuss
striking differences between bosons and fermions. Furthermore, beyond
many-particle Fock states on input, we consider arbitrary pure initial states
and derive suppression laws which stem from the wave function's permutation
symmetry alone. Finally, we identify conditions for totally destructive
interference to persist when the involved particles become partially
distinguishable.
