Restricted 132-avoiding k-ary words, Chebyshev polynomials, and continued fractions

Toufik Mansour

doi:10.1016/j.aam.2005.04.003

Restricted 132-avoiding k-ary words, Chebyshev polynomials, and continued fractions

Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study generating functions for the number of n-long k-ary words that avoid both 132 and an arbitrary ℓ-ary pattern. In several interesting cases the generating function depends only on ℓ and is expressed via Chebyshev polynomials of the second kind and continued fractions.

Original language	English
Pages (from-to)	175-193
Number of pages	19
Journal	Advances in Applied Mathematics
Volume	36
Issue number	2
DOIs	https://doi.org/10.1016/j.aam.2005.04.003
State	Published - Feb 2006

Keywords

Chebyshev polynomials
Continued fractions
Forbidden subsequence
Restricted k-ary words
k-ary words

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2005.04.003

Cite this

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abstract = "We study generating functions for the number of n-long k-ary words that avoid both 132 and an arbitrary ℓ-ary pattern. In several interesting cases the generating function depends only on ℓ and is expressed via Chebyshev polynomials of the second kind and continued fractions.",

keywords = "Chebyshev polynomials, Continued fractions, Forbidden subsequence, Restricted k-ary words, k-ary words",

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KW - Chebyshev polynomials

KW - Continued fractions

KW - Forbidden subsequence

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KW - k-ary words

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Restricted 132-avoiding k-ary words, Chebyshev polynomials, and continued fractions

Abstract

Keywords

ASJC Scopus subject areas

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