In an earlier work, the authors studied pattern avoidance in colored set
partitions in the equality sense. Here we study pattern avoidance in
colored partitions in the pattern sense. We say that
contains
in the
pattern sense if
contains a copy
when the colors are
ignored and the colors on this copy of
are order isomorphic to
the colors on
. Otherwise we say that
avoids
.
We focus on patterns from
and find that many familiar
and some new integer sequences appear. We provide bijective proofs
wherever possible, and we provide formulas for computing those
sequences that are new.