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

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

2004-04-28

arxiv.org/abs/math/0404508v2

Europ. J. Combin. 27 (2006), 496-512

Mathematics

Combinatorics

16 pages

Scientific paper

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.

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