Summary: Let $n$ be an integer >=1, and let $p(n,k)$ and $P(n,k)$ count the number of partitions of $n$ into $k$ parts, and the number of partitions of $n$ into parts less than or equal to $k$, respectively. In this paper, we show that these functions are convex. The result includes the actual value of the constant of Bateman and Erdős.

11P81

integer partition, convexity