## A new companion to Capparelli’s identities and the allied inequalities

#### When/Where:

March 17 2015, 1:55 — 2:45pm at LIT 368.

#### Abstract:

We will start by the discussion of the new companion results to Capparelli’s identities found in a joint work with Prof Berkovich late 2014. Later, I will state and prove a new partition identity which is a refinement of this companion result. Then we will start the comparison of our refinement and the refinement that Alladi and Andrews proved in 1994. Lastly, I will discuss some new developments in these refinements and some related combinatorial inequalities that are still open questions to date.