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).

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• Electronic Journal of Combinatorics
• arXiv

Later work (last updated 3 October 2026)

• A. Burstein, T. Han, S. Kitaev and P. B. Zhang, On (shape-)Wilf-equivalence of certain sets of (partially ordered) patterns, Electron. J. Combin. 32 (2025). Proves the conjecture of Gao and Kitaev that this paper left open, that {12345, 12354} and {45123, 45213} are Wilf-equivalent, along with 11 of the 12 related Wilf-equivalences suggested by computations here and by Pantone.
• All citing papers on Google Scholar (4)