  Recent works of Andrews--Newman and Hopkins--Sellers unveil an interesting
relation between two partition statistics, the crank and the mex. They state
that, for a positive integer $n$, there are as many partitions of $n$ with
non-negative crank as partitions of $n$ with odd mex. In this paper, we give a
bijective proof of a generalization of this identity provided by Hopkins,
Sellers, and Stanton. Our method uses an alternative definition of the Durfee
decomposition, whose combinatorial link to the crank was recently studied by
Hopkins, Sellers, and Yee.
