Combinations as bargraphs

Toufik Mansour; Armend Sh Shabani

doi:10.47443/dml.2022.0002

Combinations as bargraphs

Toufik Mansour, Armend Sh Shabani

Department of Mathematics

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

Abstract

In this paper, we consider statistics on combinations of [n] when combinations are presented as bargraphs. The statistics we consider are cardinality of a combination, semi-perimeter, outer site-perimeter, and inner site-perimeter. We find an explicit formula for the generating function for the number of combinations of [n] according to the considered statistics. We also find an explicit formula for the total of the above statistics over all combinations of [n].

Original language	English
Pages (from-to)	106-110
Number of pages	5
Journal	Discrete Mathematics Letters
Volume	8
DOIs	https://doi.org/10.47443/dml.2022.0002
State	Published - 2022

Bibliographical note

Publisher Copyright:
© 2022 the authors.

Keywords

Bargraphs
Combinations
Inner site-perimeter
Outer site-perimeter
Site-perimeter

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.47443/dml.2022.0002

Cite this

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title = "Combinations as bargraphs",

abstract = "In this paper, we consider statistics on combinations of [n] when combinations are presented as bargraphs. The statistics we consider are cardinality of a combination, semi-perimeter, outer site-perimeter, and inner site-perimeter. We find an explicit formula for the generating function for the number of combinations of [n] according to the considered statistics. We also find an explicit formula for the total of the above statistics over all combinations of [n].",

keywords = "Bargraphs, Combinations, Inner site-perimeter, Outer site-perimeter, Site-perimeter",

author = "Toufik Mansour and Shabani, \{Armend Sh\}",

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journal = "Discrete Mathematics Letters",

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AU - Mansour, Toufik

AU - Shabani, Armend Sh

PY - 2022

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AB - In this paper, we consider statistics on combinations of [n] when combinations are presented as bargraphs. The statistics we consider are cardinality of a combination, semi-perimeter, outer site-perimeter, and inner site-perimeter. We find an explicit formula for the generating function for the number of combinations of [n] according to the considered statistics. We also find an explicit formula for the total of the above statistics over all combinations of [n].

KW - Bargraphs

KW - Combinations

KW - Inner site-perimeter

KW - Outer site-perimeter

KW - Site-perimeter

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U2 - 10.47443/dml.2022.0002

DO - 10.47443/dml.2022.0002

M3 - Article

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SP - 106

EP - 110

JO - Discrete Mathematics Letters

JF - Discrete Mathematics Letters

ER -

Combinations as bargraphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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