Nine classes of pattern-avoiding uniquely sorted permutations are enumerated via bijections with Dyck, S-Motzkin, and Schröder paths, confirming Defant's conjectures.
Bousquet-Mélou, Multi-statistic enumeration of two -stack sortable permutations
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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.