Cell patterns in integer partitions

Toufik Mansour; Armend Sh Shabani; Daniel Yaqubi

doi:10.25596/jalc-2019-051

Cell patterns in integer partitions

Toufik Mansour, Armend Sh Shabani, Daniel Yaqubi

Department of Mathematics

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

Abstract

A partition of a positive integer n is a finite nonincreasing sequence of positive integers whose sum is n. Integer partitions can be graphically represented through Ferrers diagrams (graphs). These diagrams may contain smaller partitions, defined as cell patterns. In this paper, we study the number of different types of cell patterns lying entirely in partitions of n. Using the generating functions method we will enumerate integer partitions according to cell patterns of several types.

Original language	English
Pages (from-to)	51-63
Number of pages	13
Journal	Journal of Automata, Languages and Combinatorics
Volume	24
Issue number	1
DOIs	https://doi.org/10.25596/jalc-2019-051
State	Published - 2019

Bibliographical note

Publisher Copyright:
© Institut für Informatik Justus-Liebig-Universität Giessen.

Keywords

Bargraphs
Partitions

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Access to Document

10.25596/jalc-2019-051

Cite this

@article{b463890a119a491494862b1b540284e4,

title = "Cell patterns in integer partitions",

abstract = "A partition of a positive integer n is a finite nonincreasing sequence of positive integers whose sum is n. Integer partitions can be graphically represented through Ferrers diagrams (graphs). These diagrams may contain smaller partitions, defined as cell patterns. In this paper, we study the number of different types of cell patterns lying entirely in partitions of n. Using the generating functions method we will enumerate integer partitions according to cell patterns of several types.",

keywords = "Bargraphs, Partitions",

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

note = "Publisher Copyright: {\textcopyright} Institut f{\"u}r Informatik Justus-Liebig-Universit{\"a}t Giessen.",

year = "2019",

doi = "10.25596/jalc-2019-051",

language = "English",

volume = "24",

pages = "51--63",

journal = "Journal of Automata, Languages and Combinatorics",

issn = "1430-189X",

publisher = "Institut fur Informatik, Justus-Liebig-Universitat Giessen",

number = "1",

}

TY - JOUR

T1 - Cell patterns in integer partitions

AU - Mansour, Toufik

AU - Shabani, Armend Sh

AU - Yaqubi, Daniel

N1 - Publisher Copyright: © Institut für Informatik Justus-Liebig-Universität Giessen.

PY - 2019

Y1 - 2019

N2 - A partition of a positive integer n is a finite nonincreasing sequence of positive integers whose sum is n. Integer partitions can be graphically represented through Ferrers diagrams (graphs). These diagrams may contain smaller partitions, defined as cell patterns. In this paper, we study the number of different types of cell patterns lying entirely in partitions of n. Using the generating functions method we will enumerate integer partitions according to cell patterns of several types.

AB - A partition of a positive integer n is a finite nonincreasing sequence of positive integers whose sum is n. Integer partitions can be graphically represented through Ferrers diagrams (graphs). These diagrams may contain smaller partitions, defined as cell patterns. In this paper, we study the number of different types of cell patterns lying entirely in partitions of n. Using the generating functions method we will enumerate integer partitions according to cell patterns of several types.

KW - Bargraphs

KW - Partitions

UR - http://www.scopus.com/inward/record.url?scp=85073269375&partnerID=8YFLogxK

U2 - 10.25596/jalc-2019-051

DO - 10.25596/jalc-2019-051

M3 - Article

AN - SCOPUS:85073269375

SN - 1430-189X

VL - 24

SP - 51

EP - 63

JO - Journal of Automata, Languages and Combinatorics

JF - Journal of Automata, Languages and Combinatorics

IS - 1

ER -

Cell patterns in integer partitions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this