  Quantum interference of correlated particles is a fundamental quantum
phenomenon which carries signatures of the statistics properties of the
particles, such as bunching or anti-bunching. In presence of particular
symmetries, interference effects take place with high visibility, one of the
simplest cases being the suppression of coincident detection in the
Hong-Ou-Mandel effect. Tichy et al. recently demonstrated a simple sufficient
criterion for the suppression of output events in the more general case of
Fourier multi-port beam splitters. Here we study the case in which $2^q$
particles (either bosonic or fermionic) are injected simultaneously in
different ports of a Sylvester interferometer with $2^p \geq 2^q$ modes. In
particular, we prove a necessary and sufficient criterion for a significant
fraction of output states to be suppressed, for specific input configurations.
This may find application in assessing the indistinguishability of multiple
single photon sources and in the validation of boson sampling machines.
