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 $X\wr Y$ 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 $X\wr Y$ is also finitely based. Additionally, we indicate a general construction for basis elements in the case where $X\wr Y$ is not finitely based.