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dc.contributor.authorDornian, Patrick
dc.date.accessioned2016-04-28 19:30:11 (GMT)
dc.date.available2016-04-28 19:30:11 (GMT)
dc.date.issued2016-04-28
dc.date.submitted2016-04-25
dc.identifier.urihttp://hdl.handle.net/10012/10417
dc.description.abstractThis thesis aims to give the reader an introduction and overview of the cd-index of a poset, as well as establish some new results. We give a combinatorial proof of Ehrenborg and Karu's cd-index subdivision decomposition for Gorenstein* complexes and extend it to a wider class of subdivisions. In doing so, we define a local cd-index that behaves analogously to the well studied local h-vector. We examine known cd-index and h-vector bounds, and then use the local cd-index to bound a particular class of polytopes with the cd-index of a stacked polytope. We conclude by investigating the h-vector and local h- vector of posets in full generality, and use an algebra morphism developed by Bayer and Ehrenborg to demonstrate the structural connection between the cd-index subdivision decomposition and the local h-vector subdivision decomposition.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectdiscrete mathen
dc.subjectcombinatoricsen
dc.subjectposetsen
dc.subjectpolytopesen
dc.subjectpure mathen
dc.titleSubdividing the cd-indexen
dc.typeMaster Thesisen
dc.pendingfalse
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degree.disciplineCombinatorics and Optimizationen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws.comment.hiddenThe thesis acceptance form should be on the way over, it was just submitted by my department's Admin Coordinater Melissa Cambridge today,en
uws.contributor.advisorKatz, Eric
uws.contributor.affiliation1Faculty of Mathematicsen
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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