A STUDY OF FUNDAMENTAL COMBINATORIAL PRINCIPLES, THEIR APPLICATIONS AND SOME OF THEIR EXTENSIONS TO MULTISETS
A STUDY OF FUNDAMENTAL COMBINATORIAL PRINCIPLES, THEIR APPLICATIONS AND SOME OF THEIR EXTENSIONS TO MULTISETS
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Date
2009-10
Authors
DUNARI, MUTARI HARUNA
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Abstract
Traditionally, 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.
Description
A 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, ZARIA
Keywords
STUDY,, FUNDAMENTAL,, COMBINATORIAL,, PRINCIPLES,, APPLICATIONS,, EXTENSIONS,, MULTISETS