  We derive functional equations for distributions of six classical statistics
(ascents, descents, left-to-right maxima, right-to-left maxima, left-to-right
minima, and right-to-left minima) on separable and irreducible separable
permutations. The equations are used to find a third degree equation for joint
distribution of ascents and descents on separable permutations that generalizes
the respective known result for the descent distribution. Moreover, our general
functional equations allow us to derive explicitly (joint) distribution of any
subset of maxima and minima statistics on irreducible, reducible and all
separable permutations. In particular, there are two equivalence classes of
distributions of a pair of maxima or minima statistics. Finally, we present
three unimodality conjectures about distributions of statistics on separable
permutations.
