Restricted permutations and Chebyshev polynomials.

We study generating functions for the number of permutations in Sn subject to two restrictions. One of the restrictions belongs to S3, while the other to Sk. It turns out that in a large variety of cases the answer can be expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05

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