Permutations with forbidden subsequences and a generalized Schro"der number

Abstract Using the technique of generating trees, we prove that there are exactly 10 classes of pattern avoiding permutations enumerated by the large Schroder numbers. For each integer, m ⩾1, a sequence which generalizes the Schroder and Catalan numbers is shown to enumerate m+2 2 classes of pattern avoiding permutations. Combinatorial interpretations in terms of binary trees and polyominoes and a generating function for these sequences are given.