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

Kitaev, Sergey and Remmel, Jeffrey and Riehl, Manda (2013) On a pattern avoidance condition for the wreath product of cyclic groups with symmetric groups. ISRN Combinatorics, 2013.

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Abstract

In this paper, we extend, to a non-consecutive case, the study of the pattern matching condition on the wreath product Ck o Sn of the cyclic group Ck and the symmetric group Sn initiated in [2]. 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, which is the number of elements in C2 o Sn bi-avoiding simultaneously (1-2,0 0) and (1-2,0 1).