We describe a new method for finding patterns in permutations that produce a given pattern after the permutation has been passed once through a stack. We use this method to describe West-3-stack-sortable permutations, that is, permutations that are sorted by three passes through a stack. We also show how the method can be applied to the bubble-sort operator. The method requires the use of mesh patterns, introduced by Branden and Claesson (2011), as well as a new type of generalized pattern we call a decorated pattern.

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Additional material

• A talk given at the Computer and Information Sciences Departmental Seminar at Strathclyde University, October 2011
  
• A talk given at the ICE-TCS Seminar at Reykjavik University, October 2011
  
• Mesh patterns for checking Theorem 4.6