A family of classes in nested chain abacus and related generating functions

Abacus model has been employed widely to represent partitions for any positive integer. However, no study has been carried out to develop connected beads of abacus in graphical representation for discrete objects. To resolve this connectedness problem this study is oriented in characterising n - con...

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Main Author:	Mohommed, Eman F.
Format:	Thesis
Language:	eng eng eng
Published:	2017
Subjects:	QA Mathematics
Online Access:	https://etd.uum.edu.my/6882/1/DepositPermission_s900179.pdf https://etd.uum.edu.my/6882/2/s900179_01.pdf https://etd.uum.edu.my/6882/3/s900179_02.pdf
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id	my-uum-etd.6882
record_format	uketd_dc
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng eng
advisor	Ibrahim, Haslinda Ahmad, Nazihah Mahmood, Ammar Seddiq
topic	QA Mathematics
spellingShingle	QA Mathematics Mohommed, Eman F. A family of classes in nested chain abacus and related generating functions
description	Abacus model has been employed widely to represent partitions for any positive integer. However, no study has been carried out to develop connected beads of abacus in graphical representation for discrete objects. To resolve this connectedness problem this study is oriented in characterising n - connected objects knows as n connected ominoes, which then generate nested chain abacus. Furthermore, the theoretical conceptual properties for the nested chain abacus are being formulated. Along the construction, three different types of transformation are being created that are essential in building a family of classes. To enhance further, based on theses classes, generating functions are also being formulated by employing enumeration of combinatorial objects (ECO). In ECO method, each object is obtained from smaller object by making some local expansions. These local expansions are described in a simple way by a succession rule which can be translated into a function equation for the generating function. In summary, this stud has succeeded in producing novel graphical representation of nested chain abacus, which can be applied in tiling finite grid.
format	Thesis
qualification_name	Ph.D.
qualification_level	Doctorate
author	Mohommed, Eman F.
author_facet	Mohommed, Eman F.
author_sort	Mohommed, Eman F.
title	A family of classes in nested chain abacus and related generating functions
title_short	A family of classes in nested chain abacus and related generating functions
title_full	A family of classes in nested chain abacus and related generating functions
title_fullStr	A family of classes in nested chain abacus and related generating functions
title_full_unstemmed	A family of classes in nested chain abacus and related generating functions
title_sort	family of classes in nested chain abacus and related generating functions
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2017
url	https://etd.uum.edu.my/6882/1/DepositPermission_s900179.pdf https://etd.uum.edu.my/6882/2/s900179_01.pdf https://etd.uum.edu.my/6882/3/s900179_02.pdf
_version_	1747828122180386816
spelling	my-uum-etd.68822021-08-18T04:04:43Z A family of classes in nested chain abacus and related generating functions 2017 Mohommed, Eman F. Ibrahim, Haslinda Ahmad, Nazihah Mahmood, Ammar Seddiq Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA Mathematics Abacus model has been employed widely to represent partitions for any positive integer. However, no study has been carried out to develop connected beads of abacus in graphical representation for discrete objects. To resolve this connectedness problem this study is oriented in characterising n - connected objects knows as n connected ominoes, which then generate nested chain abacus. Furthermore, the theoretical conceptual properties for the nested chain abacus are being formulated. Along the construction, three different types of transformation are being created that are essential in building a family of classes. To enhance further, based on theses classes, generating functions are also being formulated by employing enumeration of combinatorial objects (ECO). In ECO method, each object is obtained from smaller object by making some local expansions. These local expansions are described in a simple way by a succession rule which can be translated into a function equation for the generating function. In summary, this stud has succeeded in producing novel graphical representation of nested chain abacus, which can be applied in tiling finite grid. 2017 Thesis https://etd.uum.edu.my/6882/ https://etd.uum.edu.my/6882/1/DepositPermission_s900179.pdf text eng public https://etd.uum.edu.my/6882/2/s900179_01.pdf text eng public https://etd.uum.edu.my/6882/3/s900179_02.pdf text eng public Ph.D. doctoral Universiti Utara Malaysia Abramovich, S. (2012). Partitions of integers, ferrers-young diagrams, and represen- tational efficacy of spreadsheet modeling. Spreadsheets in Education (eJSiE), 5(2), 1-27. 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A family of classes in nested chain abacus and related generating functions

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