Restricted permutations and Chebyshev polynomials.

By T. Mansour, A. Vainshtein. 2000

56 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/1836cdc1ef5880c92b328c2ac796114d088d61d7