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{\bf Robert Brignall}
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{\bf Wreath Products of Permutation Classes}
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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.
\bye