# Alexander Berkovich

## Non-negative Thoughts

#### When/Where:

February 28, 2017, 3:00 — 3:50 pm at LIT 368.

#### Abstract:

I discuss some new  inequalities involving certain  partitions with simple restrictions on largest and smallest parts. I will employ  these inequalities to show that

$$\displaystyle \sum_{n>0} \frac{q^{n(n+1)/2}}{(-q;q)_n(1-q^{L+n})(q;q)_L}$$

has non-negative  q-series coefficients for all positive integers $$L$$.

This talk is based on my current joint work with Ali K.  Uncu.