  We give three proofs of the following result conjectured by Carriegos, De
Castro-Garc\'{\i}a and Mu\~noz Casta\~neda 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 $(\alpha,
\beta)$ such that $\binom{k+1}{2} + |\alpha| + |\beta| = n$.
