Permutations sortable by n-4 passes through a stack
  We characterise and enumerate permutations that are sortable by n-4 passes through a stack. We conjecture the number of permutations sortable by n-5 passes, and also the form of a formula for the general case n-k, which involves a polynomial expression. 
Anders Claesson, Mark Dukes, Einar Steingrimsson