Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations
arXiv:1908.04025 · doi:10.46298/dmtcs.6494
Abstract
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.
23 pages, 18 figures; reformatted for Discrete Mathematics & Theoretical Computer Science