Counting 1 × 2 rectangles in set partitions

Nenad Cakić; Toufik Mansour; Armend Sh Shabani

doi:10.1080/10236198.2019.1619712

Counting 1 × 2 rectangles in set partitions

Nenad Cakić
, Toufik Mansour
, Armend Sh Shabani

Department of Mathematics

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

Abstract

In this paper, we study the generating function for the number of partitions of [n] = {1, 2, . . . , n}, represented geometrically as bargraphs, according to the number of 1 × 2 rectangles contained within the area subtended. In particular, we find both an explicit and an asymptotic formula for the total number of 1 × 2) rectangles taken over all partitions of [n].

Original language	English
Pages (from-to)	708-715
Number of pages	8
Journal	Journal of Difference Equations and Applications
Volume	25
Issue number	5
DOIs	https://doi.org/10.1080/10236198.2019.1619712
State	Published - 4 May 2019

Bibliographical note

Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

Bargraphs
generating functions
rectangle
set partitions

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1080/10236198.2019.1619712

Cite this

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abstract = "In this paper, we study the generating function for the number of partitions of [n] = \{1, 2, . . . , n\}, represented geometrically as bargraphs, according to the number of 1 × 2 rectangles contained within the area subtended. In particular, we find both an explicit and an asymptotic formula for the total number of 1 × 2) rectangles taken over all partitions of [n].",

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AU - Shabani, Armend Sh

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N2 - In this paper, we study the generating function for the number of partitions of [n] = {1, 2, . . . , n}, represented geometrically as bargraphs, according to the number of 1 × 2 rectangles contained within the area subtended. In particular, we find both an explicit and an asymptotic formula for the total number of 1 × 2) rectangles taken over all partitions of [n].

AB - In this paper, we study the generating function for the number of partitions of [n] = {1, 2, . . . , n}, represented geometrically as bargraphs, according to the number of 1 × 2 rectangles contained within the area subtended. In particular, we find both an explicit and an asymptotic formula for the total number of 1 × 2) rectangles taken over all partitions of [n].

KW - Bargraphs

KW - generating functions

KW - rectangle

KW - set partitions

UR - https://www.scopus.com/pages/publications/85066109454

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DO - 10.1080/10236198.2019.1619712

M3 - Article

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JF - Journal of Difference Equations and Applications

IS - 5

ER -

Counting 1 × 2 rectangles in set partitions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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