Two permutation classes enumerated by the central binomial coefficients

Marilena Barnabei, Flavio Bonetti, Matteo Silimbani

We define a map between the set of permutations that avoid either the four patterns $3214,3241,4213,4231$ or $3124,3142,4123,4132$, and the set of Dyck prefixes. This map, when res…