Dyck paths and restricted permutations

Toufik Mansour; Eva Y.P. Deng; Rosena R.X. Du

doi:10.1016/j.dam.2006.02.004

Dyck paths and restricted permutations

Toufik Mansour, Eva Y.P. Deng, Rosena R.X. Du

Department of Mathematics

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

Abstract

This paper is devoted to characterize permutations with forbidden patterns by using canonical reduced decompositions, which leads to bijections between Dyck paths and S_n ( 321 ) and S_n ( 231 ), respectively. We also discuss permutations in S_n avoiding two patterns, one of length 3 and the other of length k. These permutations produce a kind of discrete continuity between the Motzkin and the Catalan numbers.

Original language	English
Pages (from-to)	1593-1605
Number of pages	13
Journal	Discrete Applied Mathematics
Volume	154
Issue number	11
DOIs	https://doi.org/10.1016/j.dam.2006.02.004
State	Published - 1 Jul 2006

Bibliographical note

Funding Information:
This work was done under the auspices of the 973 Project on Mathematical Mechanization of the Ministry of Science and Technology, and the National Science Foundation of China.

Keywords

Canonical reduced decomposition
Dyck path
Restricted permutation

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2006.02.004

Cite this

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abstract = "This paper is devoted to characterize permutations with forbidden patterns by using canonical reduced decompositions, which leads to bijections between Dyck paths and Sn ( 321 ) and Sn ( 231 ), respectively. We also discuss permutations in Sn avoiding two patterns, one of length 3 and the other of length k. These permutations produce a kind of discrete continuity between the Motzkin and the Catalan numbers.",

keywords = "Canonical reduced decomposition, Dyck path, Restricted permutation",

author = "Toufik Mansour and Deng, {Eva Y.P.} and Du, {Rosena R.X.}",

note = "Funding Information: This work was done under the auspices of the 973 Project on Mathematical Mechanization of the Ministry of Science and Technology, and the National Science Foundation of China.",

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PY - 2006/7/1

Y1 - 2006/7/1

N2 - This paper is devoted to characterize permutations with forbidden patterns by using canonical reduced decompositions, which leads to bijections between Dyck paths and Sn ( 321 ) and Sn ( 231 ), respectively. We also discuss permutations in Sn avoiding two patterns, one of length 3 and the other of length k. These permutations produce a kind of discrete continuity between the Motzkin and the Catalan numbers.

AB - This paper is devoted to characterize permutations with forbidden patterns by using canonical reduced decompositions, which leads to bijections between Dyck paths and Sn ( 321 ) and Sn ( 231 ), respectively. We also discuss permutations in Sn avoiding two patterns, one of length 3 and the other of length k. These permutations produce a kind of discrete continuity between the Motzkin and the Catalan numbers.

KW - Canonical reduced decomposition

KW - Dyck path

KW - Restricted permutation

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DO - 10.1016/j.dam.2006.02.004

M3 - Article

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JF - Discrete Applied Mathematics

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ER -

Dyck paths and restricted permutations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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