Restricted permutations and Chebyshev polynomials
classification
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keywords
chebyshevpermutationspolynomialsrestrictionsanswerbelongscasesexpressed
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We study generating functions for the number of permutations in $\SS_n$ subject to two restrictions. One of the restrictions belongs to $\SS_3$, while the other to $\SS_k$. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind.
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