Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials

Sergi Elizalde; Toufik Mansour

doi:10.1016/j.disc.2005.10.010

Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials

Sergi Elizalde, Toufik Mansour

Department of Mathematics

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

Abstract

We say that a permutation π is a Motzkin permutation if it avoids 132 and there do not exist a<b such that πa<πb<πb+1. We study the distribution of several statistics in Motzkin permutations, including the length of the longest increasing and decreasing subsequences and the number of rises and descents. We also enumerate Motzkin permutations with additional restrictions, and study the distribution of occurrences of fairly general patterns in this class of permutations.

Original language	English
Pages (from-to)	170-189
Number of pages	20
Journal	Discrete Mathematics
Volume	305
Issue number	1-3
DOIs	https://doi.org/10.1016/j.disc.2005.10.010
State	Published - 6 Dec 2005

Bibliographical note

Funding Information:
We would like to thank Marc Noy for helpful comments and suggestions. The first author was partially supported by a MAE fellowship.

Keywords

Chebyshev polynomial
Generalized pattern
Motzkin path
Motzkin permutation
Permutation statistic
Restricted permutation

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2005.10.010

Cite this

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title = "Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials",

abstract = "We say that a permutation π is a Motzkin permutation if it avoids 132 and there do not exist a",

keywords = "Chebyshev polynomial, Generalized pattern, Motzkin path, Motzkin permutation, Permutation statistic, Restricted permutation",

author = "Sergi Elizalde and Toufik Mansour",

note = "Funding Information: We would like to thank Marc Noy for helpful comments and suggestions. The first author was partially supported by a MAE fellowship. ",

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AU - Mansour, Toufik

N1 - Funding Information: We would like to thank Marc Noy for helpful comments and suggestions. The first author was partially supported by a MAE fellowship.

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AB - We say that a permutation π is a Motzkin permutation if it avoids 132 and there do not exist a

KW - Chebyshev polynomial

KW - Generalized pattern

KW - Motzkin path

KW - Motzkin permutation

KW - Permutation statistic

KW - Restricted permutation

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U2 - 10.1016/j.disc.2005.10.010

DO - 10.1016/j.disc.2005.10.010

M3 - Article

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JF - Discrete Mathematics

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Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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