In this paper we consider the rank generating function of a separable
permutation Ο in the weak Bruhat order on the two intervals [id,Ο] and [Ο,w0β], where w0β=n,(nβ1),...,1. We show a surprising
result that the product of these two generating functions is the generating
function for the symmetric group with the weak order. We then obtain explicit
formulas for the rank generating functions on [id,Ο] and [Ο,w0β], which leads to the rank-symmetry and unimodality of the two graded
posets