A Simple Bijection Between 231-Avoiding and 312-Avoiding Placements

Stankova and West proved in 2002 that the patterns \( 231 \) and \( 312 \) are shape-Wilf-equivalent. Their proof was nonbijective. We give a new characterization of \( 231 \) and \( 312 \) avoiding full rook placements and use this to give a simple bijection that demonstrates the shape-Wilf-equivalence.