On a pattern avoidance condition for the wreath product of cyclic groups with symmetric groups

2009/10/16 by Sergey Kitaev, Kitaev, Sergey, Jeffrey B. Remmel +4
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.0910.3135

arxiv created 2009/10/16 · openalex publication_date 2009/10/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we extend to a non-consecutive case, the study of the pattern matching condition on the wreath product of the cyclic group and the symmetric group initiated by the authors in a previous paper. The main focus of our paper is (colored) patterns of length 2, although a number of enumerative results for longer patterns are also presented. A new non-trivial bijective interpretation for the Catalan numbers is found, in terms of simultaneously bi-avoiding two patterns in a wreath product.

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