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

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

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Abstract

We continue the study of the generalized pattern avoidance condition for Ck ≀ Sn, the wreath product of the cyclic group Ck with the symmetric group Sn, initiated in the work by Kitaev et al., In press. Among our results, there are a number of (multivariable) generating functions both for consecutive and nonconsecutive patterns, as well as a bijective proof for a new sequence counted by the Catalan numbers.