Restricted set of patterns, continued fractions, and Chebyshev polynomials
classification
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keywords
chebyshevcontinuedfractionspolynomialsrestrictionsanswerbelongscases
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We study generating functions for the number of permutations in $S_n$ subject to set of restrictions. One of the restrictions belongs to $S_3$, while the others to $S_k$. It turns out that in a large variety of cases the answer can be expressed via continued fractions, and Chebyshev polynomials of the second kind.
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