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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
DOI
https://doi.org/10.25710/q7mz-nw82
Publisher
Western Washington University
OCLC Number
842971752
Subject – LCSH
Minkowski geometry; Set theory; Convex domains; Convex bodies
Format
application/pdf
Genre/Form
masters theses
Language
English
Rights
Copying of this document 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.
Recommended Citation
Mesikepp, Tim, "M-addition" (2013). WWU Graduate School Collection. 275.
https://cedar.wwu.edu/wwuet/275