On the Diagram of Schröder Permutations

Abstract

Egge and Mansour have recently studied permutations which avoid $1243$ and $2143$ regarding the occurrence of certain additional patterns. Some of the open questions related to their work can easily be answered by using permutation diagrams. As for $132$-avoiding permutations the diagram approach gives insights into the structure of $\{1243,2143\}$-avoiding permutations that yield simple proofs for some enumerative results concerning forbidden patterns in such permutations.