Show simple item record

dc.contributorPfeifle, Julián
dc.contributor.authorCano Córdoba, Filip
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.description.abstractA 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.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
dc.subject.otherEhrhart polynomials
dc.subject.otherGeneralized permutohedron
dc.subject.otherEhrhart positivity
dc.subject.otherPolytope theory
dc.subject.otherAlgebra of Polyhedra
dc.subject.otherBrion's theorem
dc.titleAn Introduction to Polytope Theory through Ehrhart's Theorem
dc.typeMaster thesis
dc.subject.amsClassificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedra
dc.rights.accessOpen Access
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística

Files in this item


This item appears in the following Collection(s)

Show simple item record

Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain