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Enumeration of pattern-avoiding objects is an active area of study withconnections to such disparate regions of mathematics as Schubert varieties andstack-sortable sequences. Recent research in this area has brought attention tocolored permutations and colored set partitions. A colored partition of a set$S$ is a partition of $S$ with each element receiving a color from the set$[k]=\{1,2,...,k\}$. Let $\Pi_n\wr C_k$ be the set of partitions of $[n]$ withcolors from $[k]$.  In an earlier work, the authors study pattern avoidance in colored setpartitions in the equality sense. Here we study pattern avoidance in coloredpartitions in the pattern sense. We say that $\sigma\in\Pi_n\wr C_k$ contains$\pi\in \Pi_m\wr C_\ell$ in the pattern sense if $\sigma$ contains a copy $\pi$when the colors are ignored and the colors on this copy of $\pi$ are orderisomorphic to the colors on $\pi$. Otherwise we say that $\sigma$ avoids $\pi$.  We focus on patterns from $\Pi_2\wr C_2$ and find that many familiar and somenew integer sequences appear. We provide bijective proofs wherever possible,and we provide formulas for computing those sequences that are new.

Avoiding colored partitions of two elements in the pattern sense