# Sun Kim

Affiliation: University of Illinois

Email: sunkim2@illinois.edu

Title Of Talk: Bressoud's Conjecture

Abstract: By employing Andrews' generalization of Watson's $q$-analogue of Whipple's theorem, D. M. Bressoud obtained an analytic identity, which specializes to most of the well known theorems on partitions with part congruence conditions and difference conditions. This led him to define two partition functions $A$ and $B$ depending on multiple parameters as combinatorial counterparts of his identity. Bressoud then proved that $A=B$ for $\lambda=0,1$, and $\lambda=k=r=2,$ and conjectured that $A=B$ holds true for any $k\ge r\ge \lambda\ge 2$. In this talk, we discuss Bressoud's conjecture for even $\lambda$.