A four parameter generalization of Gollnitz's (BIG) partition theorem

Alladi, Krishnaswami; Andrews, George E.; Berkovich, Alexander

A four parameter generalization of Gollnitz's (BIG) partition theorem

Authors

Alladi, Krishnaswami

Andrews, George E.

Berkovich, Alexander

Description

We announce a new four parameter partition theorem from which the (big) theorem of Gollnitz follows by setting any one of the parameters equal to 0. This settles a problem of Andrews who asked whether there exists a result that goes beyond the partition theorem of Gollnitz. We state a four parameter q-series identity (key identity) which is the generating function form of this theorem. In a subsequent paper, the proof of the new four parameter key identity will be given.
9 pages