Partitions of a set satisfying certain set of conditions

Toufik Mansour; Nohad Mbarieky

doi:10.1016/j.disc.2009.02.010

Partitions of a set satisfying certain set of conditions

Toufik Mansour, Nohad Mbarieky

Department of Mathematics

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

Abstract

In this paper we present a new combinatorial class enumerated by Catalan numbers. More precisely, we establish a bijection between the set of partitions π₁ π₂ ⋯ π_n of [n] such that π_{i + 1} - π_i ≤ 1 for all i =, 1, 2 ..., n - 1, and the set of Dyck paths of semilength n. Moreover, we find an explicit formula for the generating function for the number of partitions π₁ π₂ ⋯ π_n of [n] such that either π_{i + ℓ} - π_i ≤ 1 for all i = 1, 2, ..., n - ℓ, or π_{i + 1} - π_i ≤ m for all i = 1, 2, ..., n - 1.

Original language	English
Pages (from-to)	4481-4488
Number of pages	8
Journal	Discrete Mathematics
Volume	309
Issue number	13
DOIs	https://doi.org/10.1016/j.disc.2009.02.010
State	Published - 6 Jul 2009

Keywords

Catalan numbers
Dyck paths
Partitions of a set

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2009.02.010

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AB - In this paper we present a new combinatorial class enumerated by Catalan numbers. More precisely, we establish a bijection between the set of partitions π1 π2 ⋯ πn of [n] such that πi + 1 - πi ≤ 1 for all i =, 1, 2 ..., n - 1, and the set of Dyck paths of semilength n. Moreover, we find an explicit formula for the generating function for the number of partitions π1 π2 ⋯ πn of [n] such that either πi + ℓ - πi ≤ 1 for all i = 1, 2, ..., n - ℓ, or πi + 1 - πi ≤ m for all i = 1, 2, ..., n - 1.

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ER -

Partitions of a set satisfying certain set of conditions

Abstract

Keywords

ASJC Scopus subject areas

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