Papers › Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding
Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding
Christian Bean, Émile Nadeau, Jay Pantone, Henning Ulfarsson
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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.
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