In this paper we examine the sorting operator T(LnR)=T(R)T(L)n. Applying
this operator to a permutation is equivalent to passing the permutation
reversed through a stack. We prove theorems that characterise t-revstack
sortability in terms of patterns in a permutation that we call zigzag
patterns. Using these theorems we characterise those permutations of length n
which are sorted by t applications of T for t=0,1,2,n−3,n−2,n−1. We
derive expressions for the descent polynomials of these six classes of
permutations and use this information to prove Steingr\'imsson's sorting
conjecture for those six values of t. Symmetry and unimodality of the descent
polynomials for general t-revstack sortable permutations is also proven and
three conjectures are given