The ehrhart polynomial of zonohedron and its application

Dissertant

Ftekhan, Manar Musab

Thesis advisor

Salman, Shadha Assaad

University

University of Technology

Faculty

-

Department

Applied Sciences Department

University Country

Iraq

Degree

Master

Degree Date

2013

English Abstract

Some basic mathematical tools such as convex sets, polytopes and combinatorial topology, are used quite heavily in applied fields such as geometric modeling, meshing, computer vision, medical imaging and robotics.

It is intended for a broad audience of mathematically inclined.

A polytope plays a central role in different areas of mathematics; therefore we shall take a polytope with one kind of them, which is known as a Zonohedron.

The matroid and arithmetic matroid with their properties are also given.

The concept of the Platonic solids is introduced with their properties.

Multiplicity Tutte polynomial and Ehrhart polynomial for a Zonohedron Z(X) in 2- dimension and 3-dimensions are introduced.

Theorem for the relation between the numbers of integral points of a Zonohedron and the set of generating vectors is proved.

Combinatorial interpretation of the associated multiplicity Tutte polynomial with different examples is presented to demonstrate our results.

The expression ‘duality’ means a mapping between points and plans (or vertices and faces) is introduced, together with the computation of the Ehrhart polynomial for the dual of Zonohedron and platonic solid.

Main Subjects

Mathematics

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-420182