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

University of Haifa

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	American 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

Keywords

Bargraphs
C-vertices
Combinatorial statistic
Generating functions

All Science Journal Classification (ASJC) codes

General Mathematics

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10.3906/mat-1803-113

Cite this

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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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JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

IS - 5

ER -

Bargraphs in bargraphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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