Sorting and preimages of pattern classes
In preparation
We introduce an algorithm to determine when a sorting operation, such as
stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a
new proof of the description of West-2-stack-sortable permutations, that is
permutations that are completely sorted when passed twice through a stack, in
terms of patterns. We also solve the long-standing problem of describing
West-3-stack-sortable permutations. This requires a new type of generalized
permutation pattern we call a decorated pattern.
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Presentations
Additional material
- FPSAC 2012 Extended abstract (an abstract of this paper and this paper)