Finite Differences of the Logarithm of the Partition Function

William Y. C. Chen, Larry X. W. Wang, Gary Y. B. Xie

Let $p(n)$ denote the partition function. DeSalvo and Pak proved that $\frac{p(n-1)}{p(n)}\left(1+\frac{1}{n}\right)>\frac{p(n)}{p(n+1)}$ for $n\ge 2$, as conjectured by Chen. Mo…