Two-stack-sorting with pop stacks
We consider the set of permutations that are sortable after two passes through a pop stack. We characterize these permutations in terms of forbidden patterns (classical and barred) and enumerate them according to the ascent statistic. Then we show these permutations to be in bijection with a special family of polyominoes. As a consequence, the permutations sortable by this machine are shown to have the same enumeration as three classical permutation classes.
Pudwell, Lara and Smith, Rebecca, "Two-stack-sorting with pop stacks" (2018). Mathematics and Statistics Faculty Publications. 58.