Journal of Integer Sequences, Vol. 15 (2012), Article 12.6.2 |

Department of Mathematics

Minnesota State University Moorhead

Moorhead, MN 56563

USA

Lara K. Pudwell

Department of Mathematics and Computer Science

Valparaiso University

Valparaiso, IN 46383

USA

**Abstract:**

Enumeration of pattern-avoiding objects is an active area of study with
connections to such disparate regions of mathematics as Schubert
varieties and stack-sortable sequences. Recent research in this area
has brought attention to colored permutations and colored set
partitions. A colored partition of a set is a partition of with
each element receiving a color from the set
. Let
be the set of partitions of with colors from
.

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.

(Concerned with sequences A000027 A000079 A000110 A000898 A000918 A001861 A005425 A005843 A011965 A014322 A052889 A052944 A081124.)

Received March 17 2012;
revised version received June 9 2012.
Published in *Journal of Integer Sequences*, June 13 2012.

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