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A width problem concerning convex sets with lattice point constraints
Author
Tan, June Hwee Chiat
Supervisor
Awyong, Poh Wah
Abstract
At the turn of this century, Minkowski published his famous Convex Body Theorem which became the basis for the geometry of numbers. Since the theorem first appeared, numerous modifications and variations have been made, giving rise to many inequalities for lattice constrained convex sets. In this thesis, we examine a result that was motivated by Minkowski's theorem.
In Chapter 1, we give a brief introduction to the history of convex sets with lattice point constraints. We also include some important notation and definitions which will be used throughout the thesis. In Chapter 2, we describe the main tools used in solving our thesis problem. In Chapter 3, we give the proof of a width result obtained by Scott (1973) for the square lattice. In the final chapter, we outline the scope for future research in this area. It will be seen that many new and intriguing problems remain unsolved in the area of convex sets with lattice point constraints.
In Chapter 1, we give a brief introduction to the history of convex sets with lattice point constraints. We also include some important notation and definitions which will be used throughout the thesis. In Chapter 2, we describe the main tools used in solving our thesis problem. In Chapter 3, we give the proof of a width result obtained by Scott (1973) for the square lattice. In the final chapter, we outline the scope for future research in this area. It will be seen that many new and intriguing problems remain unsolved in the area of convex sets with lattice point constraints.
Date Issued
1998
Call Number
QA171.5 Tan
Date Submitted
1998