A new four parameter q-series identity and its partition implications

Abstract

We prove a new four parameter q-hypergeometric series identity from which the three parameter key identity for the Goellnitz theorem due to Alladi, Andrews, and Gordon, follows as a special case by setting one of the parameters equal to 0. The new identity is equivalent to a four parameter partition theorem which extends the deep theorem of Goellnitz and thereby settles a problem raised by Andrews thirty years ago. Some consequences including a quadruple product extension of Jacobi's triple product identity, and prospects of future research are briefly discussed.

25 pages, in Sec. 3 Table 1 is added, discussion is added at the end of Sec. 5, minor stylistic changes, typos eliminated. To appear in Inventiones Mathematicae

References in corpus (1)

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

Cited by in corpus (3)

• Beyond Göllnitz' Theorem I: A Bijective Approach
• A combinatorial proof of the Alladi-Gordon key identity for Schur's partition theorem
• An iterative-bijective approach to generalizations of Schur's theorem