Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding
Electronic Journal of Combinatorics, Volume 31, Issue 3, 2024
Christian, Émile, Jay and Henning
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 (2019) and of Chen and Lin (2024).