dc.contributor Mier Vinué, Anna de dc.contributor.author Hakim, Sahar dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2019-01-31T11:52:45Z dc.date.available 2019-01-31T11:52:45Z dc.date.issued 2019-01 dc.identifier.uri http://hdl.handle.net/2117/128027 dc.description.abstract Matroids 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.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::Matemàtica discreta::Combinatòria dc.subject.lcsh Combinatorial analysis dc.subject.other Matroids dc.subject.other Tutte polynomial dc.subject.other Discrete Mathematics dc.subject.other Combinatorics dc.subject.other Activities dc.title Activities and coefficients of the Tutte polynomial dc.type Master thesis dc.subject.lemac Combinacions (Matemàtica) dc.subject.ams Classificació AMS::05 Combinatorics dc.identifier.slug FME-1727 dc.rights.access Open Access dc.date.updated 2019-01-23T06:25:53Z dc.audience.educationlevel Màster dc.audience.mediator Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística dc.audience.degree MÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)
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