Keith Grizzell

Affiliation: University of Florida

Email: grizzell@ufl.edu

Title Of Talk: Some Delicate Partition Inequalities

Abstract: In recent work of Alexander Berkovich and myself, we showed that for any $L>0$ and any odd $y>1$, the $q$-series expansion of
$$
\frac{1}{(q,q^{y+2},q^{2y};q^{2y+2})_L} - \frac{1}{(q^2,q^{y},q^{2y+1};q^{2y+2})_L}
$$
has non-negative coefficients. The proof involved an injective argument, but this argument cannot be used directly to prove a similar statement for even $y>2$. In my talk I will examine why the same argument fails for even $y$, and I will discuss what can be done to obtain an injection that works around the problems that an even $y$ presents.

Last update made Sun Oct 21 14:14:29 EDT 2012.
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