FINITE GEOMETRIES

Author: MARTÍ MIRAS RICARD.
Year: 2005.
University: AUTÓNOMA DE BARCELONA.
Place of defense: Facultad de Ciencias.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: It describes the function generator in the number of orbits n-conjuntos to design a space on a finite body, bathroom action group linear. The main theorem describes this function generator from the various subtypes that are classified elements of the group according to the linear structure of poset of subvariedades linear and invariant own (maximal respect the order of automorfimo restricted to the range). As implementation of these results are obtained explicit formulas for the number of classes linear codes of fixed length and dimension.

Author: VALENZUELA TRIPODORO JUAN CARLOS.
Year: 2005.
University: SEVILLA.
Place of defense: E.T.S. DE ARQUITECTURA.

Summary: The objectives of this thesis can be framed within the Theory of Extremal Grafos. One of the most famous problems in this area is the so-called problem Turán consisting of studying the possible size of a graph free subgraphs complete. They have also been emerging over the past few years various problems extremales as prolonged or widespread problem Turán. It is this kind of problem in which the study focuses reflected in this report. In particular, he examines one of these extensions called Problem Turán with contraction edges or Problem Turán juvenile complete, which is seeking to attract the largest possible size of a graph of order n is not contractible even complete graph of order p , ie without contain a subgrafo from which to obtain a complete graph with p vertices through a finite amount of contractions of edges. In parallel, as in any extremal problem, the question arises as to characterize those graphs reach such extreme value, called glyphs extremales. It also discusses two generalizations of the problem Turán to bipartite graphs: the Problem of Zarankiewicz and the Problem of Turán in bipartite graphs. In this case it comes to obtaining the highest number of edges in a bipartite graph so that it does not contain a subgrafo bipartisan complete Ks, t.