"Pattern Avoidance in Ordered Set Partitions" by Anant Godbole, Adam Goyt et al.
 

Pattern Avoidance in Ordered Set Partitions

Document Type

Article

Publication Date

1-1-2014

Description

In this paper we consider the enumeration of ordered set partitions avoiding a permutation pattern of length 2 or 3. We provide an exact enumeration for avoiding the permutation 12. We also give exact enumeration for ordered partitions with 3 blocks and ordered partitions with n-1 blocks avoiding a permutation of length 3. We use enumeration schemes to recursively enumerate 123-avoiding ordered partitions with any block sizes. Finally, we give some asymptotic results for the growth rates of the number of ordered set partitions avoiding a single pattern; including a Stanley-Wilf type result that exhibits existence of such growth rates.

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