Geodesic
Describing West-3-Stack-Sortable Permutations with Permutation Patterns
Séminaire lotharingien de combinatoire, Tome 67 (2012-2015)

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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 Brändén and Claesson (2011), as well as a new type of generalized pattern we call a decorated pattern. 

@article{SLC_2012-2015_67_a3,
     author = {Henning \'Ulfarsson},
     title = {Describing {West-3-Stack-Sortable} {Permutations} with {Permutation} {Patterns}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {67},
     year = {2012-2015},
     url = {http://geodesic.mathdoc.fr/item/SLC_2012-2015_67_a3/}
}
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JO  - Séminaire lotharingien de combinatoire
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%F SLC_2012-2015_67_a3
Henning Úlfarsson. Describing West-3-Stack-Sortable Permutations with Permutation Patterns. Séminaire lotharingien de combinatoire, Tome 67 (2012-2015). http://geodesic.mathdoc.fr/item/SLC_2012-2015_67_a3/