## A new companion to Göllnitz’ (Big) partition theorem

Speaker: Prof. Krishnaswami Alladi
Date: 03/05/2016
Time: 15:00 - 16:00

Location: RISC Seminar room

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.