Nine classes of pattern-avoiding uniquely sorted permutations are enumerated via bijections with Dyck, S-Motzkin, and Schröder paths, confirming Defant's conjectures.
Bóna, A survey of stack-sorting disciplines
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Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations
Nine classes of pattern-avoiding uniquely sorted permutations are enumerated via bijections with Dyck, S-Motzkin, and Schröder paths, confirming Defant's conjectures.