A Simple Bijective Proof of the Shape-Wilf-Equivalence of the Patterns   231 and 312
  Stankova and West proved in 2002 that the patterns 231 and 312 are shape-Wilf-equivalent. Their proof was nonbijective and fairly complicated. We give a new characterization of 231 and 312 avoiding full rook placements and use this to give a simple bijective proof of the shape-Wilf- equivalence. 
Jonathan Bloom, Dan Saracino
math.CO