Wreath products of permutation classes

Abstract

A permutation class which is closed under pattern involvement may be described in terms of its basis. The wreath product construction X VerticalTilde Y of two permutation classes X and Y is also closed, and we exhibit a family of classes Y with the property that, for any finitely based class X, the wreath product X VerticalTilde Y is also finitely based. Additionally, we indicate a general construction for basis elements in the case where X VerticalTilde Y is not finitely based.