An iterative-bijective approach to generalizations of Schur's theorem

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.