The Perimeter of 2-Compositions

Toufik Mansour; Armend Sh Shabani

doi:10.2989/16073606.2019.1648324

The Perimeter of 2-Compositions

Toufik Mansour, Armend Sh Shabani

Department of Mathematics

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

Abstract

In this note, we consider several statistics on 2-compositions. We show that there is a bijection between the set of 2-compositions and a set of bargraphs, introduced in this note, named 2-bargraphs. As we focus on the statistic per–the perimeter of the given 2-bargraph, we find the corresponding generating function. We also find an explicit formula for the total length of the perimeter over all 2-bargraphs with n-cells.

Original language	English
Pages (from-to)	1639-1644
Number of pages	6
Journal	Quaestiones Mathematicae
Volume	43
Issue number	11
DOIs	https://doi.org/10.2989/16073606.2019.1648324
State	Published - 2020

Bibliographical note

Publisher Copyright:
© 2019 NISC (Pty) Ltd.

Keywords

2-compositions
Bargraphs
perimeter

ASJC Scopus subject areas

Mathematics (miscellaneous)

Access to Document

10.2989/16073606.2019.1648324

Cite this

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title = "The Perimeter of 2-Compositions",

abstract = "In this note, we consider several statistics on 2-compositions. We show that there is a bijection between the set of 2-compositions and a set of bargraphs, introduced in this note, named 2-bargraphs. As we focus on the statistic per–the perimeter of the given 2-bargraph, we find the corresponding generating function. We also find an explicit formula for the total length of the perimeter over all 2-bargraphs with n-cells.",

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AB - In this note, we consider several statistics on 2-compositions. We show that there is a bijection between the set of 2-compositions and a set of bargraphs, introduced in this note, named 2-bargraphs. As we focus on the statistic per–the perimeter of the given 2-bargraph, we find the corresponding generating function. We also find an explicit formula for the total length of the perimeter over all 2-bargraphs with n-cells.

KW - 2-compositions

KW - Bargraphs

KW - perimeter

UR - https://www.scopus.com/pages/publications/85073961694

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ER -

The Perimeter of 2-Compositions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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