A double bounded key identity for Goellnitz's (big) partition theorem
Abstract
Given integers i,j,k,L,M, we establish a new double bounded qseries identity from which the three parameter (i,j,k) key identity of AlladiAndrewsGordon 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2000
 arXiv:
 arXiv:math/0007001
 Bibcode:
 2000math......7001A
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Number Theory;
 Mathematics  Quantum Algebra;
 05a15;
 05a19;
 11p81;
 11p82;
 11p83
 EPrint:
 17 pages, to appear in Proceedings of Gainesville 1999 Conference on Symbolic Computations