Restricted Dumont permutations, Dyck paths, and noncrossing partitions

Alexander Burstein; Sergi Elizalde; Toufik Mansour

Restricted Dumont permutations, Dyck paths, and noncrossing partitions

Alexander Burstein, Sergi Elizalde, Toufik Mansour

Department of Mathematics

Research output: Contribution to conference › Paper › peer-review

Abstract

We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is in turn a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding certain patterns of length 3 and 4 and give a natural bijection between 3142-avoiding Dumont permutations of the second kind and noncrossing partitions that uses cycle decomposition, as well as bijections between 132-, 231- and 321-avoiding Dumont permutations and Dyck paths.

Original language	English
Pages	363-374
Number of pages	12
State	Published - 2006
Event	18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006 - San Diego, CA, United States Duration: 19 Jun 2006 → 23 Jun 2006

Conference

Conference	18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006
Country/Territory	United States
City	San Diego, CA
Period	19/06/06 → 23/06/06

Keywords

Dumont permutations
Dyck paths
Forbidden subsequences
Noncrossing partitions

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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abstract = "We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is in turn a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding certain patterns of length 3 and 4 and give a natural bijection between 3142-avoiding Dumont permutations of the second kind and noncrossing partitions that uses cycle decomposition, as well as bijections between 132-, 231- and 321-avoiding Dumont permutations and Dyck paths.",

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AU - Burstein, Alexander

AU - Elizalde, Sergi

AU - Mansour, Toufik

PY - 2006

Y1 - 2006

N2 - We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is in turn a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding certain patterns of length 3 and 4 and give a natural bijection between 3142-avoiding Dumont permutations of the second kind and noncrossing partitions that uses cycle decomposition, as well as bijections between 132-, 231- and 321-avoiding Dumont permutations and Dyck paths.

AB - We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is in turn a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding certain patterns of length 3 and 4 and give a natural bijection between 3142-avoiding Dumont permutations of the second kind and noncrossing partitions that uses cycle decomposition, as well as bijections between 132-, 231- and 321-avoiding Dumont permutations and Dyck paths.

KW - Dumont permutations

KW - Dyck paths

KW - Forbidden subsequences

KW - Noncrossing partitions

UR - http://www.scopus.com/inward/record.url?scp=84860606643&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:84860606643

SP - 363

EP - 374

T2 - 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006

Y2 - 19 June 2006 through 23 June 2006

ER -

Restricted Dumont permutations, Dyck paths, and noncrossing partitions

Abstract

Conference

Keywords

ASJC Scopus subject areas

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