Restricted 132-alternating permutations and Chebyshev polynomials

Details Restricted 132-alternating permutations and Chebyshev polynomials Restricted 132-alternating permutations and Chebyshev polynomials

2002-10-04

arxiv.org/abs/math/0210058v1

Mathematics

Combinatorics

22 pages

Scientific paper

A permutation is said to be \emph{alternating} if it starts with rise and then descents and rises come in turn. In this paper we study the generating function for the number of alternating permutations on $n$ letters that avoid or contain exactly once 132 and also avoid or contain exactly once an arbitrary pattern on $k$ letters. In several interesting cases the generating function depends only on $k$ and is expressed via Chebyshev polynomials of the second kind.

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