  Andrews and Newman have recently introduced the notion of the mex of a
partition, the smallest positive integer that is not a part. The concept has
been used since at least 2011, though, with connections to Frobenius symbols.
Recently the parity of the mex has been associated to the crank statistic named
by Dyson in 1944. In this note, we extend and strengthen the connection between
the crank and mex (along with a new generaliztion of the mex) by proving a
number of properties that naturally relate these partition statistics.
