Some Properties of Simplicial Geometries

Simple item page
dc.contributor.advisorLawrence, James
dc.contributor.authorMerrick, Cynthia
dc.creatorMerrick, Cynthia
dc.date.accessioned2013-08-19T21:16:34Z
dc.date.available2013-08-19T21:16:34Z
dc.date.issued2013-08
dc.description.abstractSimplicial geometries, whose points are the collection of all k-element subsets of a given (finite) ground set, were described in 1970 by Crapo and Rota [5]. So far, only geometries for which k =2 and their duals have been well-studied. In this paper, I address many general questions about simplicial geometries on n vertices, via matroid properties such as the structure of circuits, minors and orientability. I describe the smallest largely unstudied simplicial geometry, on a ground set of six vertices, with k = 3, which I call G^6_3. A construction of the only (up to symmetry) non-contractible basis is given, as well as a complete characterization of all circuits that can be built using six or fewer vertices. I prove that the matroid of G^6_3 is ternary, and give two large deleted minors which are regular. I also explore more than one method for nding topes of the associated arrangement of hyperplanes, and describe a specific construction for a simplicial tope.
dc.format.extent85 pages
dc.identifier.urihttps://hdl.handle.net/1920/8360
dc.language.isoen
dc.rightsCopyright 2013 Cynthia Merrick
dc.subjectMathematics
dc.subjectCombinatorial geometry
dc.subjectMatroid
dc.subjectOriented matroid
dc.subjectSimplicial geometry
dc.subjectSimplicial matroid
dc.titleSome Properties of Simplicial Geometries
dc.typeDissertation
thesis.degree.disciplineMathematics
thesis.degree.grantorGeorge Mason University
thesis.degree.levelDoctoral

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Merrick_gmu_0883E_10421.pdf
Size:
498.96 KB
Format:
Adobe Portable Document Format
Download

Collections

College of Science