Restricted 132-alternating permutations and Chebyshev polynomials

T. Mansour

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arXiv · math/0210058

Restricted 132-alternating permutations and Chebyshev polynomials

T. Mansour

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Abstract

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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BibTeX RIS

T. Mansour. 2002-10-04. Restricted 132-alternating permutations and Chebyshev polynomials. https://arxiv.org/abs/math/0210058

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