2011•arXiv (Cornell University)Open access

A Simple Bijective Proof of the Shape-Wilf-Equivalence of the Patterns 231 and 312

Jonathan Bloom, Dan Saracino

Abstract

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.

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Key concepts: Bijection, Equivalence (formal languages), Simple (philosophy), Mathematics, Combinatorics, Characterization (materials science), Pure mathematics, Discrete mathematics