2011/03/01 by Adam M. Goyt, Lara Pudwell, Goyt, Adam M. +2
Mathematics · #05A18 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.CO #msc:05A18
paper · pdf · doi:10.48550/arxiv.1103.0239
24 pages, 3 tables, to appear in the Permutation Patterns 2010 Proceedings, a special issue of Pure Mathematics and Applications
openalex publication_date 2011/03/01 · arxiv created 2011/08/12 · arxiv updated 2011/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Pattern avoidance in the symmetric group Sn has provided a number of useful connections between seemingly unrelated problems from stack-sorting to Schubert varieties. Recent work has generalized these results to Sn\wr Cc, the objects of which can be viewed as "colored permutations". Another body of research that has grown from the study of pattern avoidance in permutations is pattern avoidance in Πn, the set of set partitions of [n]. Pattern avoidance in set partitions is a generalization of the well-studied notion of noncrossing partitions. Motivated by recent results in pattern avoidance in Sn \wr Cc we provide a catalog of initial results for pattern avoidance in colored partitions, Πn \wr Cc. We note that colored set partitions are not a completely new concept. Signed (2-colored) set partitions appear in the work of Björner and Wachs involving the homology of partition lattices. However, we seek to study these objects in a new enumerative context.