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arXiv · 1707.07809

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

Benjamin Gunby·Dömötör Pálvölgyi
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Abstract

We consider asymptotics of set partition pattern avoidance in the sense of Klazar. Our main result derives the asymptotics of the number of set partitions avoiding a given set partition within an exponential factor, which leads to a classification of possible growth rates of set partition pattern classes. We further define a notion of permutation-tuple avoidance, which generalizes notions of Aldred et al. and the usual permutation pattern setting, and similarly determine the number of permutation-tuples avoiding a given tuple to within an exponential factor.

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Benjamin Gunby, Dömötör Pálvölgyi. 2017-07-25. Asymptotics of Pattern Avoidance in the Klazar Set Partition and Permutation-Tuple Settings. https://arxiv.org/abs/1707.07809

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