Restricted set of patterns, continued fractions, and Chebyshev polynomials

Details Restricted set of patterns, continued fractions, and Chebyshev polynomials Restricted set of patterns, continued fractions, and Chebyshev polynomials

2001-08-06

arxiv.org/abs/math/0108043v1

Mathematics

Combinatorics

9 pages

Scientific paper

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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