Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations

Defant, Engen, and Miller defined a permutation to be uniquely sorted if ithas exactly one preimage under West's stack-sorting map. We enumerate classesof uniquely sorted permutations that avoid a pattern of length three and apattern of length four by establishing bijections between these classes andvarious lattice paths. This allows us to prove nine conjectures of Defant.Comment: 23 pages, 18 figures; reformatted for Discrete Mathematics & Theoretical Computer Scienc