A STUDY OF FUNDAMENTAL COMBINATORIAL PRINCIPLES, THEIR APPLICATIONS AND SOME OF THEIR EXTENSIONS TO MULTISETS

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dc.contributor.authorDUNARI, MUTARI HARUNA
dc.date.accessioned2014-02-24T11:58:04Z
dc.date.available2014-02-24T11:58:04Z
dc.date.issued2009-10
dc.descriptionA THESIS SUBMITTED TO THE POSTGRADUATE SCHOOL, AHMADU BELLO UNIVERSITY ZARIA-NIGERIA, IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF MASTER OF SCIENCE DEGREE IN MATHEMATICS DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE AHMADU BELLO UNIVERSITY, ZARIAen_US
dc.description.abstractTraditionally, combinatorial identities along side with their applications in graph and design theory are seen to constitute the ingredients of combinatorics. The properties of finite set must lie at the heart of any study of combinatorial theory. Considering all these and the enormous applications of multisets in mathematics, computer science and linguistics, it has become pertinent to conduct studies in the area most especially from the combinatorial point of view. Combinatorics of multisets provide explicit solutions to a host of mathematical problems and programming problems in computer science. The aim of this thesis is to conduct a comprehensive study of the fundamental principles of combinatorics, their applications and some of their extensions to multisets. Accordingly, the following chapters are presented:  Chapter one gives a general introduction and discusses some mathematical preliminaries required in dealing with combinatorial problems. A novel approach (Wikipedia) for introducing relations and functions in their combinatorial form is discussed. Finally, a comprehensive method to define specifically the “closure” of a transitve relation is outlined.  Chapter two provides a comprehensive literature review.  Chapter three discusses the basic combinatorial principles with some few illustrations of their applications. In this section we have raised a new problem and provided a partial solution.  Chapter four deals with essentials of multisets and multiset theory. Essentially, this section deals with the basics of multisets and emphasizes the related issues. In particular, a method to compute the power multiset of a given multiset is outlined.  Chapter five considers some combinatorial applications of multisets. In this section we have closely studied the work done in[SS 03] and found that the results are quite innovative.  Chapter six gives the conclusion and some future directions.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/2411
dc.language.isoenen_US
dc.subjectSTUDY,en_US
dc.subjectFUNDAMENTAL,en_US
dc.subjectCOMBINATORIAL,en_US
dc.subjectPRINCIPLES,en_US
dc.subjectAPPLICATIONS,en_US
dc.subjectEXTENSIONS,en_US
dc.subjectMULTISETSen_US
dc.titleA STUDY OF FUNDAMENTAL COMBINATORIAL PRINCIPLES, THEIR APPLICATIONS AND SOME OF THEIR EXTENSIONS TO MULTISETSen_US
dc.typeThesisen_US
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