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

Benjamin Gunby
<span title="2019-06-23">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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 π such that the number of set partitions of [n] avoiding π 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
more &raquo; ... s and Tardos's 2004 proof of the Stanley-Wilf Conjecture.
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