On bijections between 231-avoiding permutations and Dyck paths

Abstract

We construct a bijection between 231-avoiding permutations and Dyck paths that sends the sum of the major index and the inverse major index of a 231-avoiding permutation to the major index of the corresponding Dyck path. Furthermore, we relate this bijection to others and exhibit a bistatistic on 231-avoiding permutations which is related to the q,t-Catalan numbers.

13 pages, the author is very grateful to Matteo Silimbani for providing a proof of Conjecture 5.10