dc.contributor Pfeifle, Julián dc.contributor.author Cano Córdoba, Filip dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2019-10-31T12:19:49Z dc.date.available 2019-10-31T12:19:49Z dc.date.issued 2019-10 dc.identifier.uri http://hdl.handle.net/2117/171328 dc.description.abstract A classic introduction to polytope theory is presented, serving as the foundation to develop more advanced theoretical tools, namely the algebra of polyhedra and the use of valuations. The main theoretical objective is the construction of the so called Berline-Vergne valuation. Most of the theoretical development is aimed towards this goal. A little survey on Ehrhart positivity is presented, as well as some calculations that lead to conjecture that generalized permutohedra have positive coefficients in their Ehrhart polynomials. Throughout the thesis three different proofs of Ehrhart's theorem are presented, as an application of the new techniques developed. dc.language.iso eng dc.publisher Universitat Politècnica de Catalunya dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria dc.subject.lcsh Polyhedra dc.subject.lcsh Polytopes dc.subject.other Ehrhart polynomials dc.subject.other Generalized permutohedron dc.subject.other Ehrhart positivity dc.subject.other Polytope theory dc.subject.other Algebra of Polyhedra dc.subject.other Brion's theorem dc.title An Introduction to Polytope Theory through Ehrhart's Theorem dc.type Master thesis dc.subject.lemac Políedres dc.subject.lemac Politops dc.subject.ams Classificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedra dc.identifier.slug FME-1814 dc.rights.access Open Access dc.date.updated 2019-10-16T17:06:04Z dc.audience.educationlevel Màster dc.audience.mediator Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
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