The ehrhart polynomial of zonohedron and its application

مقدم أطروحة جامعية

Ftekhan, Manar Musab

مشرف أطروحة جامعية

Salman, Shadha Assaad

الجامعة

الجامعة التكنولوجية

الكلية

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القسم الأكاديمي

قسم العلوم التطبيقية

دولة الجامعة

العراق

الدرجة العلمية

ماجستير

تاريخ الدرجة العلمية

2013

الملخص الإنجليزي

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.

التخصصات الرئيسية

الرياضيات

• APA
• MLA
• AMA

لغة النص

الإنجليزية

نوع البيانات

رسائل جامعية

رقم السجل

BIM-420182