Restricted set of patterns, continued fractions, and Chebyshev polynomials

Abstract

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.

9 pages

References in corpus (3)

• Permutations with restricted patterns and Dyck paths
• Layered restrictions and Chebyshev polynomials
• Restricted 132-avoiding permutations