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

2016/09/20 by Benjamin Gunby, Gunby, Benjamin
Mathematics · #05A05 #05A16 #05A18 #05D40 #06A06 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1609.06023

openalex publication_date 2016/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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 Marcus and Tardos's 2004 proof of the Stanley-Wilf Conjecture.

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