*Abstract:* |
Title: A new companion to Göllnitz' (Big) partition theorem
Speaker: Professor Krishnaswami Alladi
University of Florida, USA
Time and Location: Tuesday, March 3, 2016
Seminar room castle, RISC, Hagenberg
Abstract:
One of the deepest results in the theory of partitions
is a 1967 theorem of Göllnitz. This theorem is often viewed an
``the next level'' partition theorem beyond Schur's classical
1926 partition theorem. In 1993 Alladi-Gordon provided a new
approach to Schur's theorem by introducing a technique called
{\it{the method of weighted words}}. Then in 1995, Alladi-Andrews-Gordon
applied this method to Göllnitz' theorem to obtain a significant
refinement and generalization. This also explained clearly why
Göllnitz' theorem is the next level result beyond Schur, but much
deeper. In 1968 and 69, starting with Schur's theorem,
Andrews obtained two infinite hierarchies of partition theorems,
which are dual to each other. In that spirit, Alladi-Andrews recently
discovered (and proved) a dual of Göllnitz' theorem. We will discuss
the contruction of this dual both combinatorially and explain it
in a q-hypergeometric setting. |