ABSTRACT
Stack sorting of permutations has been the subject of intensive research. It is concerned with the operation of sorting permutations by passing them through a stack. This chapter restricts attention to the most vigorously studied version, that is sometimes called West stack sorting, or right-greedy stack sorting. There are at least two reasons for which this version of stack sorting is the subject of more work than other versions. First, there are three equivalent and natural ways of defining this stack sorting operation, which enables to use at least three different sets of methods when proving results about stack sorting. Second, there are numerous conjectures about the operation that are very easy to state, yet very difficult to prove. The connections between stack sorting and pattern avoidance are strong, but not particularly surprising.
