  We start with a bijective proof of Schur's theorem due to Alladi and Gordon
and describe how a particular iteration of it leads to some very general
theorems on colored partitions. These theorems imply a number of important
results, including Schur's theorem, Bressoud's generalization of a theorem of
G\"ollnitz, two of Andrews' generalizations of Schur's theorem, and the
Andrews-Olsson identities.
