  In a general, multi-mode scattering setup, we show how the permutation
symmetry of a many-particle input state determines those scattering unitaries
which exhibit strictly suppressed many-particle transition events. We formulate
purely algebraic suppression laws that identify these events and show that the
many-particle interference at their origin is robust under weak disorder and
imperfect indistinguishability of the interfering particles. Finally, we
demonstrate that all suppression laws so far described in the literature are
embedded in the general framework that we here introduce.
