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arXiv · 1609.06023

Asymptotics of Pattern Avoidance in the Permutation-Tuple and Klazar Set Partition Settings

Benjamin Gunby
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Abstract

We consider asymptotics of set partition pattern avoidance in the sense of Klazar. One of the results of this paper extends work of Alweiss, and finds a classification for set partitions $\pi$ such that the number of set partitions of $[n]$ avoiding $\pi$ grows more slowly than $n^{cn}$ for all $c>0$. Several conjectures are proposed, and the related question of asymptotics of parallel ($k$-tuple) permutation pattern avoidance is considered and solved completely to within an exponential factor, generalizing Marcus and Tardos's 2004 proof of the Stanley-Wilf Conjecture.

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Benjamin Gunby. 2016-09-20. Asymptotics of Pattern Avoidance in the Permutation-Tuple and Klazar Set Partition Settings. https://arxiv.org/abs/1609.06023

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