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.

Published: J. Combin. Math. Combin. Comput., 2012, arXiv.