A unifying combinatorial approach to refined little Göllnitz and Capparelli's
companion identities
Abstract.
In this talk, we introduce a new class of partitions, called $k$-strict partitions. By
applying both horizontal and vertical dissections of Ferrers diagrams with appropriate
labellings, we derive combinatorially the weighted generating function for $k$-strict partitions
and $k$-strict partitions with distinct parts. This enables us to give a unified combinatorial
treatment of Berkovich-Uncu's companion of the well-known Capparelli identities as well as
their refinements of Savage-Sills' new little G\"{o}llnitz identities. This is joint work with
Jiang Zeng.