Pattern Avoidance in Ordered Set Partitions
Combinatorics
2013-03-26 v2
Abstract
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 that exhibits existence of such growth rates.
Cite
@article{arxiv.1212.2530,
title = {Pattern Avoidance in Ordered Set Partitions},
author = {Anant Godbole and Adam Goyt and Jennifer Herdan and Lara Pudwell},
journal= {arXiv preprint arXiv:1212.2530},
year = {2013}
}
Comments
19 pages, 2 figures; Now includes a proof of what was Conjecture 1, and a generalization thereof