Permutations with forbidden subsequences and a generalized Schröder number Original Research Article

Using the technique of generating trees, we prove that there are exactly 10 classes of pattern avoiding permutations enumerated by the large Schröder numbers. For each integer, m⩾1, a sequence which generalizes the Schröder and Catalan numbers is shown to enumerate m+22 classes of pattern avoiding permutations. Combinatorial interpretations in terms of binary trees and polyominoes and a generating function for these sequences are given.