Lattice Paths and Pattern-Avoiding Uniquely Sorted PermutationsArticle
Authors: Hanna Mularczyk
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Hanna Mularczyk
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.