Subclasses of the separable permutations
Bulletin of the London Mathematical Society, 43 (2011), 859–870.
With Michael Albert and Mike Atkinson.
We prove that all subclasses of the separable permutations not containing Av(231) or a symmetry of this class have rational generating functions. Our principal tools are partial well-order, atomicity, and the theory of strongly rational permutation classes introduced here for the first time.
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