TY: THES
T1 - A união de matroides: sobre dois artigos base desta operação
A1 - Herdade, Simão Matias
N2 - This Master thesis focus on two papers on the sum of matroids, chosen for their relevance on the subject. On one hand, for showing interesting results on the subject, using almost nothing but the basic concepts of the topic. On the other hand, for bringing comprehension to the importance and centrality of the other theory concepts and propositions. In practice, having that on mind, we start presenting the fundamentals of Matroids Theory and of the sum of matroids operation; also presenting integer partitions, since they are used on the first paper. With this background, we then exhibit both papers in the most simple and clear way found. Namely, in the first paper, on the µ-colorings of a matroid, we present an easier proof of each of the three main results involved. In the second one, on the notion of transversals of the sum of matroids, we also try to exhibit it in a clear way, showing in detail all the computation required, but above all, highlighting the important steps involved. Finally, we analyse the understanding brought by the two papers to the field of the sum of matroids, studying the consequences of their results, the questions they rise and steps taken forward towards their resolution. Along the way, we also approach one or two different Mathematics fields that this work naturally led us into. This is the case of the Linear Algebra conclusions obtained, as well as of one or two remarks on computation capacity.
UR - http://repositorio.ul.pt/handle/10451/1353
Y1 - 2008
PB - No publisher defined