A double bounded key identity for Goellnitz's (big) partition theorem
Combinatorics
2007-05-23 v2 Number Theory
Quantum Algebra
Abstract
Given integers i,j,k,L,M, we establish a new double bounded q-series identity from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the identity yields a strong refinement of Goellnitz's theorem with a bound on the parts given by L. This is the first time a bounded version of Goellnitz's (big) theorem has been proved. This leads to new bounded versions of Jacobi's triple product identity for theta functions and other fundamental identities.
Keywords
Cite
@article{arxiv.math/0007001,
title = {A double bounded key identity for Goellnitz's (big) partition theorem},
author = {K. Alladi and A. Berkovich},
journal= {arXiv preprint arXiv:math/0007001},
year = {2007}
}
Comments
17 pages, to appear in Proceedings of Gainesville 1999 Conference on Symbolic Computations