Hui Guo

The Log-Convexity of the $n$-th Root Sequence of the Distinct Partition Function

Let $q(n)$ denote the total number of partitions of $n$ into distinct parts and $\Delta$ be the difference operator with respect to $n$. We prove that for any real number $\alpha$, there exists an integer $n(\alpha)$ such that the sequence\ $\{\sqrt[n]{q(n)/n^{\alpha } } \}_{n\ge n(\alpha) } $ is log-convex by obtainin...