Algorithmic coincidence classification of mesh patterns

Information and Computation, Volume 292, 105014, 2023

Christian, Bjarki, Tomas and Henning

We review and extend previous results on coincidence of mesh patterns. We introduce the notion of a force on a permutation pattern and apply it to the coincidence classification of mesh patterns, completing the classification up to size three. We also show that this concept can be used to enumerate classical permutation classes.

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• Information and Computation
• arXiv

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Later work (last updated 3 October 2026)

• P. Gregor, T. Mütze and Namrata, Combinatorial generation via permutation languages. VI. Binary trees, European J. Combin. 122 (2024). To show that their algorithm generates all binary trees avoiding certain patterns, they prove a coincidence: 231 and certain mesh patterns have the same avoiders as 231 and those patterns with one box unshaded.
• All citing papers on Google Scholar (6)