  We define a map between the set of permutations that avoid either the four
patterns $3214,3241,4213,4231$ or $3124,3142,4123,4132$, and the set of Dyck
prefixes. This map, when restricted to either of the two classes, turns out to
be a bijection that allows us to determine some notable features of these
permutations, such as the distribution of the statistics "number of ascents",
"number of left-to-right maxima", "first element", and "position of the maximum
element"
