  We introduce a statistic $\pmaj$ on partitions of $[n]=\{1,2,..., n\}$, and
show that it is equidistributed with the number of 2-crossings over partitions
of $[n]$ with given sets of minimal block elements and maximal block elements.
This generalizes the classical result of equidistribution for the permutation
statistics inversion number and major index.
