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Title

M-addition

Date Permissions Signed

5-9-2013

Date of Award

2013

Document Type

Masters Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Gardner, Richard J.

Second Advisor

Ćurgus, Branko

Third Advisor

Hartenstine, David

Abstract

This study builds upon the work of Gardner, Hug and Weil [1, Section 6] by further exploring the properties of M-addition. It is shown that several well-known theorems on Minkowski addition have M-addition parallels, including results involving intersections, the valuation property and the convex hull. The last of these enables us to detail su cient conditions for when the M-sum of convex polytopes is a convex polytope. Nested operations of M-addition are also examined and an M-addition generalization of the Shapley-Folkman Lemma and a related bound are offered.

Type

Text

Publisher

Western Washington University

OCLC Number

842971752

Digital Format

application/pdf

Genre/Form

Academic theses

Language

English

Rights

Copying of this thesis in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this thesis for commercial purposes, or for financial gain, shall not be allowed without the author's written permission.

Included in

Mathematics Commons

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