Geodesic
Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations
Discrete mathematics & theoretical computer science, Permutation Patterns 2019, Tome 22 (2020-2021) no. 2.

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Defant, Engen, and Miller defined a permutation to be uniquely sorted if it has exactly one preimage under West's stack-sorting map. We enumerate classes of uniquely sorted permutations that avoid a pattern of length three and a pattern of length four by establishing bijections between these classes and various lattice paths. This allows us to prove nine conjectures of Defant. 
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Mularczyk, Hanna. Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations. Discrete mathematics & theoretical computer science, Permutation Patterns 2019, Tome 22 (2020-2021) no. 2. doi : 10.46298/dmtcs.6494. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6494/

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