We give three proofs of the following result conjectured by Carriegos, De Castro-García and Muñoz Castañeda in their work on enumeration of control systems: when $\binom{k+1}{2} \le n < \binom{k+2}{2}$, there are as many partitions of $n$ with $k$ corners as pairs of partitions $(α, β)$ such that $\binom{k+1}{2} + |α| + |β| = n$.