Layered restrictions and Chebyshev polynomials

Details Layered restrictions and Chebyshev polynomials Layered restrictions and Chebyshev polynomials

2000-08-22

arxiv.org/abs/math/0008173v2

Mathematics

Combinatorics

8 pages

Scientific paper

A permutation is called layered if it consists of the disjoint union of substrings (layers) so that the entries decrease within each layer, and increase between the layers. We find the generating function for the number of permutations on $n$ letters avoiding $(1,2,3)$ and a layered permutation on $k$ letters. In the most interesting case of two layers, the generating function depends only on $k$ and is expressed via Chebyshev polynomials of the second kind.

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