Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations
Combinatorics
2023-06-22 v4
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.
Cite
@article{arxiv.1908.04025,
title = {Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations},
author = {Hanna Mularczyk},
journal= {arXiv preprint arXiv:1908.04025},
year = {2023}
}
Comments
23 pages, 18 figures; reformatted for Discrete Mathematics & Theoretical Computer Science