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

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

2011-10-12

arxiv.org/abs/1110.2564v1

Mathematics

Combinatorics

13 pages

Scientific paper

Stankova and West proved in 2002 that the patterns 231 and 312 are
shape-Wilf-equivalent. Their proof was nonbijective and fairly compli- cated.
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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