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

University of Haifa

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	American 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

Keywords

Bargraphs
generating functions
rectangle
set partitions

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

Access to Document

10.1080/10236198.2019.1619712

Cite this

@article{fb7c3d45b8c94f73a1a155c56129e6bd,

title = "Counting 1 × 2 rectangles in set partitions",

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].",

keywords = "Bargraphs, generating functions, rectangle, set partitions",

author = "Nenad Caki{\'c} and Toufik Mansour and Shabani, \{Armend Sh\}",

note = "Publisher Copyright: {\textcopyright} 2019, {\textcopyright} 2019 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2019",

month = may,

day = "4",

doi = "10.1080/10236198.2019.1619712",

language = "American English",

volume = "25",

pages = "708--715",

journal = "Journal of Difference Equations and Applications",

issn = "1023-6198",

publisher = "Taylor and Francis Ltd.",

number = "5",

}

TY - JOUR

T1 - Counting 1 × 2 rectangles in set partitions

AU - Cakić, Nenad

AU - Mansour, Toufik

AU - Shabani, Armend Sh

PY - 2019/5/4

Y1 - 2019/5/4

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 - http://www.scopus.com/inward/record.url?scp=85066109454&partnerID=8YFLogxK

U2 - 10.1080/10236198.2019.1619712

DO - 10.1080/10236198.2019.1619712

M3 - Article

SN - 1023-6198

VL - 25

SP - 708

EP - 715

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

IS - 5

ER -

Counting 1 × 2 rectangles in set partitions

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this