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.
Highlights
We continue the study of the generalized pattern avoidance condition for CCkk ≀ SSnn, the wreath product of the cyclic group CCkk with the symmetric group SSnn, initiated in the work by Kitaev et al, In press
E goal of this paper is to continue the study of patternmatching conditions on the wreath product CCkk ≀ SSnn of the [c1y]c.liCcCkkg≀roSSunnpisCtChkkeagnrdoutpheofsykkmnnnnmn seitgrnicedgrpoeurpmuSStnnatiinointisatwedheirne there are kk signs, 1 = ωω0, ωω, ωω2,..., ωωkkkk, where ωω is a primitive kkth root of unity
We think of the elements of ww w ww1ww2 ⋯ wwnn as the colors of the corresponding elements of the underlying permutation σσ
Summary
We continue the study of the generalized pattern avoidance condition for CCkk ≀ SSnn, the wreath product of the cyclic group CCkk with the symmetric group SSnn, initiated in the work by Kitaev et al, In press. 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
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