الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The Theory of Ordered Sets has many applications in other areas of
mathematics including algebra, set theory, combinatorice and linear
programming. Also many practical problems such as scheduling has its
settings as a problem in partial orders.
In this thesis we concentrate on two main problems concerning
partially ordered sets. These problems are the dimension problem and the
jump-number problem.
- A brief description of the contents of the thesis is as follows.
In Chapter one we summarize some basic concepts, definitions and
theorems about posets.
In Chapter two we present the definition of the dimension of a
poset and study it as a parameter.
In Chapter three we introduce the concepts of optimal linear
extension, gready posets. We also study the jump-number problem for
posets.
In Chapter four we are devoted to studying jum-critical posets.
Some new results appear in this chapter, such as Theorems 4.3.1 and
4.3.2. We also give a list of one hundred sixteen 4-critical posets and this
list is partially proved to complete.
Finally, the algorithm which determines the optimal linear
extension for a given poset is obtained in chapter 5.