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In this paper we examine the sorting operator $T(LnR)=T(R)T(L)n$. Applyingthis operator to a permutation is equivalent to passing the permutationreversed through a stack. We prove theorems that characterise $t$-revstacksortability 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 $t=0,1,2,n-3,n-2,n-1$. Wederive expressions for the descent polynomials of these six classes ofpermutations and use this information to prove Steingr\'imsson's sortingconjecture for those six values of $t$. Symmetry and unimodality of the descentpolynomials for general $t$-revstack sortable permutations is also proven andthree conjectures are given.

Revstack sort, zigzag patterns, descent polynomials of $t$-revstack sortable permutations, and Steingr\'imsson's sorting conjecture