Describing West-3-stack-sortable permutations with permutation patterns

Details Describing West-3-stack-sortable permutations with permutation patterns Describing West-3-stack-sortable permutations with permutation patterns

2011-10-06

arxiv.org/abs/1110.1219v3

Mathematics

Combinatorics

20 pages, 7 figures

Scientific paper

We describe a new method for finding patterns in permutations that produce a given pattern after the permutation has been passed once through a stack. We use this method to describe West-3-stack-sortable permutations, that is, permutations that are sorted by three passes through a stack. We also show how the method can be applied to the bubble-sort operator. The method requires the use of mesh patterns introduced by Br\"and\'en and Claesson (2011), as well as a new type of generalized pattern we call a decorated pattern.

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