A new four parameter q-series identity and its partition implications
Combinatorics
2009-11-07 v3 Number Theory
Quantum Algebra
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.
Keywords
Cite
@article{arxiv.math/0205055,
title = {A new four parameter q-series identity and its partition implications},
author = {Krishnaswami Alladi and George E. Andrews and Alexander Berkovich},
journal= {arXiv preprint arXiv:math/0205055},
year = {2009}
}
Comments
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