  Babson and Steingr\'{\i}msson introduced generalized permutation patterns and
showed that most of the Mahonian statistics in the literature can be expressed
by the combination of generalized pattern functions. Particularly, they defined
a new Mahonian statistic in terms of generalized pattern functions, which is
denoted $stat$. Recently, Amini investigated the equidistributions of these
Mahonian statistics over sets of pattern avoiding permutations. Moreover, he
posed several conjectures. In this paper, we construct a bijection from
$S_n(213)$ to $S_n(231)$, which maps the statistic $(maj,stat)$ to the
statistic $(stat,maj)$. This allows us to give solutions to some of Amini's
conjectures.
