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.
Citation Information
Godbole, Anant; Goyt, Adam; Herdan, Jennifer; and Pudwell, Lara. 2014. Pattern Avoidance in Ordered Set Partitions. Annals of Combinatorics. Vol.18(3). 429-445. https://doi.org/10.1007/s00026-014-0232-y ISSN: 0218-0006