Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding
Combinatorics
2023-12-14 v1
Abstract
We prove that any class of permutations defined by avoiding a partially ordered pattern (POP) with height at most two has a regular insertion encoding and thus has a rational generating function. Then, we use Combinatorial Exploration to find combinatorial specifications and generating functions for hundreds of other permutation classes defined by avoiding a size 5 POP, allowing us to resolve several conjectures of Gao and Kitaev and of Chen and Lin.
Cite
@article{arxiv.2312.07716,
title = {Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding},
author = {Christian Bean and Émile Nadeau and Jay Pantone and Henning Ulfarsson},
journal= {arXiv preprint arXiv:2312.07716},
year = {2023}
}