  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.
