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dc.contributorMier Vinué, Anna de
dc.contributor.authorHakim, Sahar
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.description.abstractMatroids are combinatorial objects that capture abstractly the essence of dependence. The Tutte polynomial, defined for matroids and graphs, has a numerous amount of information about these structures. In this thesis, we will introduce matroids, define them and give the most important properties they have. Then we will define the Tutte polynomial and give interesting results found in this area of research. After that we will start interpreting Tutte coefficients. First we will discuss about some specific Tutte coefficients and the relation between Tutte coefficients and parallel and series classes in a matroid. These relations were found recently for graphs, and we worked out in applying them for matroids and adding to the given results. Then we will discuss will be about a theorem linking matroid connectivity and the coefficient of x, where we have also our contribution in proving it using the activities. Finally, we will introduce Brylawski's equations. We will discuss the proof of two cases of this equation. The proof of the second equation in this section is a result of our work on this thesis.
dc.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
dc.subject.lcshCombinatorial analysis
dc.subject.otherTutte polynomial
dc.subject.otherDiscrete Mathematics
dc.titleActivities and coefficients of the Tutte polynomial
dc.typeMaster thesis
dc.subject.lemacCombinacions (Matemàtica)
dc.subject.amsClassificació AMS::05 Combinatorics
dc.rights.accessOpen Access
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística

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