Partition analysis and the little Göllnitz identites

Abstract

This work follows the spirit of Andrews' series of papers on Partition Analysis. In $2011$, Savage and Sills found new sum sides for the little Göllnitz identities and provided their partition interpretations. It turns out that similar companions exist for a mod $8$ partition identity due to Andrews. In this work, we use MacMahon's Partition Analysis to study partitions related to these identities. We find refined generating functions for them, where we keep track of the size of each part. Finally, by considering the alternating sum and Schmidt weight, we show the application of these refined functions in the study of partition statistics.