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

Access to Document

10.1016/j.aam.2005.04.003

Cite this

@article{a552d11cd25e43e78e1e83cd491fc823,

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

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",

author = "Toufik Mansour",

year = "2006",

month = feb,

doi = "10.1016/j.aam.2005.04.003",

language = "English",

volume = "36",

pages = "175--193",

journal = "Advances in Applied Mathematics",

issn = "0196-8858",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Restricted 132-avoiding k-ary words, Chebyshev polynomials, and continued fractions

AU - Mansour, Toufik

PY - 2006/2

Y1 - 2006/2

N2 - 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.

AB - 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.

KW - Chebyshev polynomials

KW - Continued fractions

KW - Forbidden subsequence

KW - Restricted k-ary words

KW - k-ary words

UR - https://www.scopus.com/pages/publications/31544439892

U2 - 10.1016/j.aam.2005.04.003

DO - 10.1016/j.aam.2005.04.003

M3 - Article

AN - SCOPUS:31544439892

SN - 0196-8858

VL - 36

SP - 175

EP - 193

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this