Bargraphs in bargraphs

Toufik Marsour; Armend Sh Shabani

doi:10.3906/mat-1803-113

Bargraphs in bargraphs

Toufik Marsour, Armend Sh Shabani

Department of Mathematics

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

Abstract

Bargraphs are lattice paths in ℕ₀ ² that start at the origin and end upon their first return to the x-axis. Each bargraph is represented by a sequence of column heights π₁π₂...π_m such that column j contains π_j cells. In this paper, we study the number of bargraphs with n cells and m columns according to the distribution for the statistic that records the number of times a given shape lies entirely within a bargraph for various small shapes.

Original language	English
Pages (from-to)	2763-2773
Number of pages	11
Journal	Turkish Journal of Mathematics
Volume	42
Issue number	5
DOIs	https://doi.org/10.3906/mat-1803-113
State	Published - 2018

Bibliographical note

Publisher Copyright:
© TÜBI˙TAK.

Keywords

Bargraphs
C-vertices
Combinatorial statistic
Generating functions

ASJC Scopus subject areas

General Mathematics

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10.3906/mat-1803-113

Cite this

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title = "Bargraphs in bargraphs",

abstract = "Bargraphs are lattice paths in ℕ0 2 that start at the origin and end upon their first return to the x-axis. Each bargraph is represented by a sequence of column heights π1π2...πm such that column j contains πj cells. In this paper, we study the number of bargraphs with n cells and m columns according to the distribution for the statistic that records the number of times a given shape lies entirely within a bargraph for various small shapes.",

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N2 - Bargraphs are lattice paths in ℕ0 2 that start at the origin and end upon their first return to the x-axis. Each bargraph is represented by a sequence of column heights π1π2...πm such that column j contains πj cells. In this paper, we study the number of bargraphs with n cells and m columns according to the distribution for the statistic that records the number of times a given shape lies entirely within a bargraph for various small shapes.

AB - Bargraphs are lattice paths in ℕ0 2 that start at the origin and end upon their first return to the x-axis. Each bargraph is represented by a sequence of column heights π1π2...πm such that column j contains πj cells. In this paper, we study the number of bargraphs with n cells and m columns according to the distribution for the statistic that records the number of times a given shape lies entirely within a bargraph for various small shapes.

KW - Bargraphs

KW - C-vertices

KW - Combinatorial statistic

KW - Generating functions

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IS - 5

ER -

Bargraphs in bargraphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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