Generalization and refinement of the Berkovich-Garvan partition inequalities

When/Where:

April 1, 2014, at 1:55pm, in LIT 368

Abstract:

In section 5 of their paper “Dissecting the Stanley Partition Function”, Profs. Berkovich and Garvan showed how to prove an infinite collection of new partition inequalities by constructing a (non-trivial) injection. I will review these inequalities and the injection they used. Then, I will look at generalizing and refining both the inequalities and the injection, in a manner akin to what Prof. Berkovich and I did in our recent paper “A partition inequality involving two \(q\)-Pochhammer symbols”. Finally, I will discuss how this method of generalization should also work in some other settings.