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- W2951467757 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 $S$ is a partition of $S$ with each element receiving a color from the set $[k]={1,2,...,k}$. Let $Pi_nwr C_k$ be the set of partitions of $[n]$ with colors from $[k]$. In an earlier work, the authors study 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 $sigmainPi_nwr C_k$ contains $piin Pi_mwr C_ell$ in the pattern sense if $sigma$ contains a copy $pi$ when the colors are ignored and the colors on this copy of $pi$ are order isomorphic to the colors on $pi$. Otherwise we say that $sigma$ avoids $pi$. We focus on patterns from $Pi_2wr C_2$ 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." @default.
- W2951467757 created "2019-06-27" @default.
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- W2951467757 date "2012-03-16" @default.
- W2951467757 modified "2023-09-27" @default.
- W2951467757 title "Avoiding colored partitions of two elements in the pattern sense" @default.
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