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{\bf M. H. Albert, R. E. L. Aldred, M. D. Atkinson, C. C. Handley, D. A. Holton and D. J. McCaughan}
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{\bf Sorting Classes}
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Weak and strong sorting classes are pattern-closed classes that are
also closed downwards under the weak and strong orders on
permutations.  They are studied using partial orders that capture both
the subpermutation order and the weak or strong order.  In both cases
they can be characterised by forbidden permutations in the appropriate
order.  The connection with the corresponding forbidden permutations
in pattern-closed classes is explored.  Enumerative results are found
in both cases.

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