Generating trees and the Catalan and Schröder numbers (Q1903733)

Let \(S_n(\tau)\) be the set of all permutations \(\pi\in S_n\) which avoid the subpattern \(\tau\). The author gives a new bijective proof of the well-known result that \(|S_n(123)|= |S_n(132)|= c_n\), the \(n\)th Catalan number. He also proves a conjecture of Shapiro and Getu that \(|S_n(3142, 2413)|\) equals the Schröder number \(S_{n- 1}\).