A four parameter generalization of Gollnitz's (BIG) partition theorem
Combinatorics
2007-05-23 v1 Number Theory
Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.math/0005157,
title = {A four parameter generalization of Gollnitz's (BIG) partition theorem},
author = {Krishnaswami Alladi and George E. Andrews and Alexander Berkovich},
journal= {arXiv preprint arXiv:math/0005157},
year = {2007}
}
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9 pages