1234-avoiding permutations and Dyck paths

Marilena Barnabei, Flavio Bonetti, Matteo Silimbani

Published 2011-02-08Version 1

We define a map $\nu$ between the symmetric group $S_n$ and the set of pairs of Dyck paths of semilength $n$. We show that the map $\nu$ is injective when restricted to the set of 1234-avoiding permutations and characterize the image of this map.