Geodesic
Asymptotic results on Klazar set partition avoidance
Discrete mathematics & theoretical computer science, Permutation Patterns 2016, Tome 19 (2017-2018) no. 2.

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We establish asymptotic bounds for the number of partitions of $[n]$ avoiding a given partition in Klazar's sense, obtaining the correct answer to within an exponential for the block case. This technique also enables us to establish a general lower bound. Additionally, we consider a graph theoretic restatement of partition avoidance problems, and propose several conjectures. 
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     author = {Alweiss, Ryan},
     title = {Asymptotic results on {Klazar} set partition avoidance},
     journal = {Discrete mathematics & theoretical computer science},
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     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-2-7/}
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Alweiss, Ryan. Asymptotic results on Klazar set partition avoidance. Discrete mathematics & theoretical computer science, Permutation Patterns 2016, Tome 19 (2017-2018) no. 2. doi : 10.23638/DMTCS-19-2-7. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-2-7/

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