321-Avoiding Permutations and Chebyshev Polynomials

Toufik Mansour

doi:10.1007/978-3-0348-7915-6_4

321-Avoiding Permutations and Chebyshev Polynomials

Toufik Mansour

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In [6] it was shown that the generating function for the number of permutations on n letters avoiding both 321 and (d + 1)(d + 2)...k12... d is given by$$ \frac{{2t{{U}_{{k - 1}}}\left( t \right)}}{{{{U}_{k}}\left( t \right)}}$$for all k > 2, 2 ≥ d + 1 ≥ k, where Um is the mth Chebyshev polynomial of the second kind and$$t = \frac{1}{{2\sqrt x }}.$$In this paper we present three different classes of 321-avoiding permutations which are enumerated by this generating function.

Original language	English
Title of host publication	Mathematics and Computer Science III
Subtitle of host publication	Trends in Mathematics
Editors	Michael Drmota, Philippe Flajolet, Danièle Gardy, Bernhard Gittenberger
Place of Publication	Basel
Publisher	Birkhauser
Pages	37-38
Number of pages	2
ISBN (Electronic)	978-3-0348-7915-6
ISBN (Print)	978-3-0348-9620-7
DOIs	https://doi.org/10.1007/978-3-0348-7915-6_4
State	Published - 2004

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10.1007/978-3-0348-7915-6_4

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title = "321-Avoiding Permutations and Chebyshev Polynomials",

abstract = "In [6] it was shown that the generating function for the number of permutations on n letters avoiding both 321 and (d + 1)(d + 2)...k12... d is given by\$\$ \textbackslash{}frac\{\{2t\{\{U\}\_\{\{k - 1\}\}\}\textbackslash{}left( t \textbackslash{}right)\}\}\{\{\{\{U\}\_\{k\}\}\textbackslash{}left( t \textbackslash{}right)\}\}\$\$for all k > 2, 2 ≥ d + 1 ≥ k, where Um is the mth Chebyshev polynomial of the second kind and\$\$t = \textbackslash{}frac\{1\}\{\{2\textbackslash{}sqrt x \}\}.\$\$In this paper we present three different classes of 321-avoiding permutations which are enumerated by this generating function.",

author = "Toufik Mansour",

year = "2004",

doi = "10.1007/978-3-0348-7915-6\_4",

language = "English",

isbn = "978-3-0348-9620-7",

pages = "37--38",

editor = "Michael Drmota and Philippe Flajolet and Dani{\`e}le Gardy and Bernhard Gittenberger",

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T1 - 321-Avoiding Permutations and Chebyshev Polynomials

AU - Mansour, Toufik

PY - 2004

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N2 - In [6] it was shown that the generating function for the number of permutations on n letters avoiding both 321 and (d + 1)(d + 2)...k12... d is given by$$ \frac{{2t{{U}_{{k - 1}}}\left( t \right)}}{{{{U}_{k}}\left( t \right)}}$$for all k > 2, 2 ≥ d + 1 ≥ k, where Um is the mth Chebyshev polynomial of the second kind and$$t = \frac{1}{{2\sqrt x }}.$$In this paper we present three different classes of 321-avoiding permutations which are enumerated by this generating function.

AB - In [6] it was shown that the generating function for the number of permutations on n letters avoiding both 321 and (d + 1)(d + 2)...k12... d is given by$$ \frac{{2t{{U}_{{k - 1}}}\left( t \right)}}{{{{U}_{k}}\left( t \right)}}$$for all k > 2, 2 ≥ d + 1 ≥ k, where Um is the mth Chebyshev polynomial of the second kind and$$t = \frac{1}{{2\sqrt x }}.$$In this paper we present three different classes of 321-avoiding permutations which are enumerated by this generating function.

U2 - 10.1007/978-3-0348-7915-6_4

DO - 10.1007/978-3-0348-7915-6_4

M3 - Chapter

SN - 978-3-0348-9620-7

SP - 37

EP - 38

BT - Mathematics and Computer Science III

A2 - Drmota, Michael

A2 - Flajolet, Philippe

A2 - Gardy, Danièle

A2 - Gittenberger, Bernhard

PB - Birkhauser

CY - Basel

ER -

321-Avoiding Permutations and Chebyshev Polynomials

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