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.
|Title of host publication||24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)|
|Place of Publication||Nancy, France|
|Number of pages||12|
|Publication status||Published - 2012|
- sorting operations
- sorting algorithm
- pattern classes
Claesson, A., & Úlfarsson, H. (2012). Sorting and preimages of pattern classes. In 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (pp. 595-606). Nancy, France.