  We use permutation-group methods plus SU(3) group-theoretic methods to
determine the action of a three-channel passive optical interferometer on
controllably delayed single-photon pulse inputs to each channel.
Permutation-group techniques allow us to relate directly expressions for rates
and, in particular, investigate symmetries in the coincidence landscape. These
techniques extend the traditional Hong-Ou-Mandel effect analysis for
two-channel interferometry to valleys and plateaus in three-channel
interferometry. Our group-theoretic approach is intuitively appealing because
the calculus of Wigner $D$ functions partially accounts for permutational
symmetries and directly reveals the connections among $D$ functions, partial
distinguishability, and immanants.
