Generating and enumerating 321-avoiding and skew-merged simple permutations

Abstract

The simple permutations in two permutation classes - the 321-avoiding per- mutations and the skew-merged permutations - are enumerated using a uniform method. In both cases, these enumerations were known implicitly, by working back- wards from the enumeration of the class, but the simple permutations had not been enumerated explicitly. In particular, the enumeration of the simple skew-merged permutations leads to the first truly structural enumeration of this class as a whole. The extension of this method to a wider collection of classes namely grid classes of infinite paths is discussed.